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# Question 25. In an A.P. the first term is 22, nth term is –11 and the sum of first n term is 66. Find n and the d, the common difference.

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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that in arithmetic progression the first term is 22, nth term is –11 and the sum of first n term is 66.

And we have to find n and the d, the common difference.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 25

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1. Given A.P. has first term(a) = 22, nth term(an) = –11 and sum(Sn) = 123.

Now by using the formula of sum of n terms of an A.P.

Sn = n[a + an] / 2

=> 66 = n[22 + (−11)]/2

66 = n[22 − 11]/2

=> 11n = 132

=> n = 12

By using the formula of nth term of an A.P.

an = a + (n – 1)d

=> −11 = 22 + (12 – 1)d

=> 11d = –33

=> d = –3

Hence, the number of terms of given A.P. is 12 and common difference is –3.

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