1. Find the sum of the first 17 natural numbers ?
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Correct Ans:289
Explanation:
1 + 3 + 5 + ... + 33
Here the first term = 1 , common difference = 2
Sum of 17 terms = (17/2) (1 + 33) = 17 x 17 = 289
2. In an arithmetic progression the first term is 10 and its common difference is 8. If the general term is a_{n} , find a_{19} - a_{11}.
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Correct Ans:64
Explanation:
Given a = 10 and common difference = 8.
General Term a_{n} = a +(n-1)d => a_{n} = 10 + 8(n-1) = 8n + 2
a_{19} = 152 + 2=154
a_{11} = 88 + 2 = 90
a_{19} - a_{11} = 64
3. In an arithmetic progression the first term is 9 and its common difference is 6. If the general term is a_{n} , find a_{17} - a_{11}.
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Correct Ans:36
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_{17} = 102 + 3=105
a_{11} = 66 + 3 = 69
a_{17} - a_{11} = 36
4. In an arithmetic progression the first term is 9 and its common difference is 7. If the general term is a_{n} , find a_{32} - a_{26}.
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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_{32} = 224 + 2=226
a_{26} = 182 + 2 = 184
a_{32} - a_{26} = 42
5. In an arithmetic progression the first term is 5 and its common difference is 3. If the general term is a_{n} , find a_{18} - a_{13}.
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Correct Ans:15
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_{18} = 54 + 2=56
a_{13} = 39 + 2 = 41
a_{18} - a_{13} = 15
6. 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
7. 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
8. 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
9. 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}) / 6 .
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Correct Ans:7
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
10. 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
11. 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
12. In an arithmetic progression the first term is 7 and its common difference is 3. If the general term is a_{n} , find a_{20} - a_{13}.
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Correct Ans:21
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_{20} = 60 + 4=64
a_{13} = 39 + 4 = 43
a_{20} - a_{13} = 21
13. 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_{14}.
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Correct Ans:24
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_{14} = 42 + 4 = 46
a_{22} - a_{14} = 24
14. In an arithmetic progression the first term is 8 and its common difference is 3. If the general term is a_{n}, find a_{42} - a_{31}.
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Correct Ans:33
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_{42} = 126 + 5=131
a_{31} = 93 + 5 = 98
a_{42} - a_{31} = 33
15. In an arithmetic progression the first term is 4 and its common difference is 2. If the general term is a_{n} , find a_{22} - a_{16}.
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Correct Ans:12
Explanation:
Given a = 4 and common difference = 2.
General Term a_{n} = a +(n-1)d => a_{n} = 4 + 2(n-1) = 2n + 2
a_{22} = 44 + 2=46
a_{16} = 32 + 2 = 34
a_{22} - a_{16} = 12
16. In an arithmetic progression the first term is 5 and its common difference is 4. If the general term is a_{n} , find a_{6} x a_{3}.
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Correct Ans:325
Explanation:
Given a = 5 and common difference = 4.
General Term a_{n} = a +(n-1)d => a_{n} = 5 + 4(n-1) = 4n + 1
a_{6} = 24 + 1= 25
a_{3} = 12 + 1 = 13
a_{6}* a_{3} = 325
17. In an arithmetic progression the first term is 21 and its common difference is 2. If the general term is a_{n} , find a_{21} - a_{14}.
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Correct Ans:14
Explanation:
Given a = 21 and common difference = 2.
General Term a_{n} = a +(n-1)d => a_{n} = 21 + 2(n-1) = 2n + 19
a_{21} = 42 + 19 = 61
a_{14} = 28 + 19 = 47
a_{21} - a_{14} = 14
18. In an arithmetic progression the first term is 11 and its common difference is 2. If the general term is a_{n} , find a_{21} - a_{13}.
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Correct Ans:16
Explanation:
Given a = 11 and common difference = 2.
General Term a_{n} = a +(n-1)d
=> a_{n} = 11 + 2(n-1) = 2n + 9
a_{21} = 42 + 9=51
a_{13} = 26 + 9 = 35
a_{21} - a_{13} = 16
19. In an arithmetic progression the first term is 7 and its common difference is 1. If the general term is a_{n} , find a_{11} - a_{8}.
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Correct Ans:3
Explanation:
Given a = 7 and common difference = 1.
General Term a_n = a +(n-1)d => a_{n} = 7 + 1(n-1) = 1n + 6
a_{11} = 11 + 6 = 17
a_{8} = 8 + 6 = 14
a_{11} - a_{8} = 3
20. In an arithmetic progression the first term is 6 and its common difference is 2. If the general term is a_{n} , find a_{10} - a_{6}.
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Correct Ans:8
Explanation:
Given a = 6 and common difference = 2.
General Term a_n = a +(n-1)d => a_{n} = 6 + 2(n-1) = 2n + 4
a_{10} = 20 + 4 = 24
a_{6} = 12 + 4 = 16
a_{10} - a_{6} = 8
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