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# Question 73. The sum of the first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is -30 and common difference is 8. Find n.

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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 that the sum of the first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is -30 and common difference is 8.

Now we have to Find the value of n.

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 73

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1. Let us assume S1 be the sum of the first n terms of an A.P.

whose first term is 8 and the common difference is 20.

Hence, S1 = n[2(8) + (n – 1)20] / 2

= n[16 + 20n – 20] / 2

= n[10n – 2]

Let us assume S2 be the sum of first 2n terms of another A.P.

whose first term is -30 and common difference is 8.

Hence, S2 = 2n[2(–30) + (2n – 1)8] / 2

= n[–60 + 16n – 8]

= n[16n – 68]

According to the question, we have

=> S1 = S2

=> n[10n – 2] = n[16n – 68]

=> 10n – 2 = 16n – 68

=> 6n = 66

=> n = 11

Hence, the value of n is 11.

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