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Progression Questions
21.
In an arithmetic progression the first term is 7 and its common difference is 6. If the general term is an , find a12 - a7.
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Correct Ans:30
Explanation:
Given a = 7 and common difference = 6.
General Term a_n = a +(n-1)d => an = 7 + 6(n-1) = 6n + 1
a12 = 72 + 1 = 73
a7 = 42 + 1 = 43
a12 - a7 = 73 - 43 = 30
General Term a_n = a +(n-1)d => an = 7 + 6(n-1) = 6n + 1
a12 = 72 + 1 = 73
a7 = 42 + 1 = 43
a12 - a7 = 73 - 43 = 30
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22. In an arithmetic progression the first term is 11 and its common difference is 2. If the general term is an , find a12 - a5.
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Correct Ans:14
Explanation:
Given a = 11 and common difference = 2.
General Term an = a +(n-1)d => an = 11 + 2(n-1) = 2n + 9
a12 = 24 + 9 = 33
a5 = 10 + 9 = 19
a12 - a5 = 33 - 19 = 14
General Term an = a +(n-1)d => an = 11 + 2(n-1) = 2n + 9
a12 = 24 + 9 = 33
a5 = 10 + 9 = 19
a12 - a5 = 33 - 19 = 14
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23. In an arithmetic progression the first term is 7 and its common difference is 2. If the general term is an ,find a7 - a3.
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Correct Ans:8
Explanation:
Given a = 7 and common difference = 2.
General Term an = a +(n-1)d => an = 7 + 2(n-1) = 2n + 5
a7 = 14 + 5 = 19
a3 = 6 + 5 = 11
a7 - a3 = 8
General Term an = a +(n-1)d => an = 7 + 2(n-1) = 2n + 5
a7 = 14 + 5 = 19
a3 = 6 + 5 = 11
a7 - a3 = 8
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24. In an arithmetic progression the first term is 6 and its common difference is 5. If the general term is an , find a6 - a4.
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Correct Ans:10
Explanation:
Given a = 6 and common difference = 5.
General Term an = a +(n-1)d => an = 6 + 5(n-1) = 5n + 1
a6 = 30 + 1= 31
a4 = 20 + 1 = 21
a6 - a4 = 10
General Term an = a +(n-1)d => an = 6 + 5(n-1) = 5n + 1
a6 = 30 + 1= 31
a4 = 20 + 1 = 21
a6 - a4 = 10
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25. In an arithmetic progression the first term is 6 and its common difference is 3. If the general term is an , find a5 - a3 ?
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Correct Ans:6
Explanation:
Given a = 6 and common difference = 3.
General Term an = a +(n-1)d => an = 6 + 3(n-1) = 3n + 3
a5 = 15 + 3 = 18
a3 = 9 + 3 = 12
a5 - a3 = 18 - 12 = 6
General Term an = a +(n-1)d => an = 6 + 3(n-1) = 3n + 3
a5 = 15 + 3 = 18
a3 = 9 + 3 = 12
a5 - a3 = 18 - 12 = 6
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26. In an arithmetic progression the first term is 9 and its common difference is 6. If the general term is (a_n) , find a_24 - a_12.
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Correct Ans:72
Explanation:
Given a = 9 and common difference = 6.
General Term a_n = a +(n-1)d
a_n = 9 + 6(n-1) = 6n + 3
a_24 = 144 + 3=147
a_12 = 72 + 3 = 75
a_24 - a_12 = 72
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27. In an arithmetic progression the first term is 8 and its common difference is 5. If the general term is (a_n) , find a_11 - a_5.
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Correct Ans:30
Explanation:
Given a = 8 and common difference = 5.
General Term a_n = a +(n-1)d
a_n = 8 + 5(n-1) = 5n + 3
a_11 = 55 + 3=58
a_5 = 25 + 3 = 28
a_11 - a_5 = 30
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28. In an arithmetic progression the first term is 9 and its common difference is 7. If the general term is (a_n) , find a_12 - a_6.
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Correct Ans:42
Explanation:
Given a = 9 and common difference = 7.
General Term a_n = a +(n-1)d
a_n = 9 + 7(n-1) = 7n + 2
a_12 = 84 + 2=86
a_6 = 42 + 2 = 44
a_12 - a_6 = 42
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29. In an arithmetic progression the first term is 7 and its common difference is 6. If the general term is (a_n) , find a_10 - a_7.
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Correct Ans:18
Explanation:
Given a = 7 and common difference = 6.
General Term a_n = a +(n-1)d
a_n = 7 + 6(n-1) = 6n + 1
a_10 = 60 + 1=61
a_7 = 42 + 1 = 43
a_10 - a_7 = 18
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30. In an arithmetic progression the first term is 6 and its common difference is 11. If the general term is (a_n) , find a_21 - a_14.
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Correct Ans:77
Explanation:
Given a = 6 and common difference = 11.
General Term a_n = a +(n-1)d
a_n = 6 + 11(n-1) = 11n + -5
a_21 = 231 + -5=226
a_14 = 154 + -5 = 149
a_21 - a_14 = 77
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31. In an arithmetic progression the first term is 8 and its common difference is 3. If the general term is (a_n) , find a_20 - a_12.
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Correct Ans:24
Explanation:
Given a = 8 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 8 + 3(n-1) = 3n + 5
a_20 = 60 + 5=65
a_12 = 36 + 5 = 41
a_20 - a_12 = 24
Workspace
32. In an arithmetic progression the first term is 9 and its common difference is 5. If the general term is (a_n) , find a_11 - a_6.
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Correct Ans:25
Explanation:
Given a = 9 and common difference = 5.
General Term a_n = a +(n-1)d
a_n = 9 + 5(n-1) = 5n + 4
a_11 = 55 + 4=59
a_6 = 30 + 4 = 34
a_11 - a_6 = 25
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33. In an arithmetic progression the first term is 7 and its common difference is 6. If the general term is (a_n) , find a_21 - a_16.
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Correct Ans:30
Explanation:
Given a = 7 and common difference = 6.
General Term a_n = a +(n-1)d
a_n = 7 + 6(n-1) = 6n + 1
a_21 = 126 + 1=127
a_16 = 96 + 1 = 97
a_21 - a_16 = 30
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34. In an arithmetic progression the first term is 12 and its common difference is 5. If the general term is (a_n) , find a_17 - a_11.
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Correct Ans:30
Explanation:
Given a = 12 and common difference = 5.
General Term a_n = a +(n-1)d
a_n = 12 + 5(n-1) = 5n + 7
a_17 = 85 + 7=92
a_11 = 55 + 7 = 62
a_17 - a_11 = 30
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35. In an arithmetic progression the first term is 11 and its common difference is 6. If the general term is (a_n) , find a_18 - a_13.
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Correct Ans:30
Explanation:
Given a = 11 and common difference = 6.
General Term a_n = a +(n-1)d
a_n = 11 + 6(n-1) = 6n + 5
a_18 = 108 + 5=113
a_13 = 78 + 5 = 83
a_18 - a_13 = 30
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36. In an arithmetic progression the first term is 11 and its common difference is 3. If the general term is (a_n) , find a_43 - a_32.
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Correct Ans:33
Explanation:
Given a = 11 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 11 + 3(n-1) = 3n + 8
a_43 = 129 + 8=137
a_32 = 96 + 8 = 104
a_43 - a_32 = 33
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37. In an arithmetic progression the first term is 5 and its common difference is 3. If the general term is (a_n) , find a_32 - a_24.
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Correct Ans:24
Explanation:
Given a = 5 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 5 + 3(n-1) = 3n + 2
a_32 = 96 + 2=98
a_24 = 72 + 2 = 74
a_32 - a_24 = 24
Workspace
38. In an arithmetic progression the first term is 7 and its common difference is 3. If the general term is (a_n) , find a_22 - a_16.
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Correct Ans:18
Explanation:
Given a = 7 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 7 + 3(n-1) = 3n + 4
a_22 = 66 + 4=70
a_16 = 48 + 4 = 52
a_22 - a_16 = 18
Workspace
39. In an arithmetic progression the first term is 7 and its common difference is 3. If the general term is (a_n) , find a_32 - a_23.
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Correct Ans:27
Explanation:
Given a = 7 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 7 + 3(n-1) = 3n + 4
a_32 = 96 + 4=100
a_23 = 69 + 4 = 73
a_32 - a_23 = 27
Workspace
40. In an arithmetic progression the first term is 6 and its common difference is 3. If the general term is (a_n) , find a_21 - a_16.
SHOW ANSWER
Correct Ans:15
Explanation:
Given a = 6 and common difference = 3.
General Term a_n = a +(n-1)d
a_n = 6 + 3(n-1) = 3n + 3
a_21 = 63 + 3=66
a_16 = 48 + 3 = 51
a_21 - a_16 = 15
Workspace
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