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If the sum of first p terms of an A.P is...

If the sum of first `p` terms of an A.P is equal to the sum of first `q` terms, then show that the sum of its first `(p+q)` terms is `zero`.`(p ne q)`.

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TARGET PUBLICATION-ARITHMETIC PROGRESSION -PRACTICE SET 3.5
  1. For a given A.P., t7=4, d=-4 then a=……… a)6 b)-7 c)20 d)28

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  2. For a given AP, a=3.5, d=0, n=101 then tn=………. a)0 b)103.5 c)104.5 d)...

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  3. In an A.P, first two terms are -3, 4, then 21st term is……….a)-143 b)14...

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  4. If for an A.P, d=5 then t18-t13=……………a)5 b)20 c)25 d30

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  5. Sum of first five multiples of 3 is……a)45 b)15 c)55 d)35

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  6. 15, 10, 5,…… In this A.P the sum of first 10 terms is…..a)-75 b)-125 c...

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  7. In an A.P, 1st term is 1 and the last term is 20.The sum of all terms ...

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  8. Find the 4th term from the end in an A.P, -11,-8,-5,….,49

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  9. In an A.P 10th term is 46, sum of 5th term and 7th term is 52. Find th...

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  10. An A.P has its 4th term as -15 and 9th term as -30. Find the sum of fi...

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  11. Two A.P's are given as 9,7,5,…. and 24,21,18,…. If nth term of both t...

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  12. If sum of 3rd and 8th term of an A.P is 7 and sum of 7th and 14th term...

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  13. In an A.P, first term is -5 and last term is 45. If sum of all the num...

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  14. Sum of 1 to n natural numbers is 36. Find the value of n.

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  15. Divide 207 in three parts, such that all parts are in A.P and product ...

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  16. There are 37 terms in an A.P. The sum of three terms placed exactly at...

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  17. If first term of an A.P is a, second term is b and last term is c, the...

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  18. If the sum of first p terms of an A.P is equal to the sum of first q t...

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  19. If m times the mth term of an A.P is equal to n times its nth term the...

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  20. ₹1000 is invested at 10 % simple interest. Check at the end of every y...

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