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Question 13. Find the sum: (v) 7 + 10 1/2 + 14 + . . . + 84

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This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6

In this question we have been given an arithmetic progression. And we have to find its sum.

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 13(v)

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1 Answer

  1. Given series is an A.P. with first term(a) = 7,

    Common difference(d) = 101/2 − 7 = (21 − 14)/2 = 7/2 and nth term(an) = 84.

    We know nth term of an A.P. is given by, an = a + (n − 1)d.

    => 84 = 7 + (n − 1)(7/2)

    => 168 = 14 + 7n − 7

    => n = 161/7

    => n = 23

    Also we know sum of n terms of an A.P. is given by Sn = n[a + an]/2.

    S23 = 23[7 + 84]/2

    = 23(91)/2

    = 2093/2 = 1046.5

    Hence, the sum of terms of the given series is 1046.5

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