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# Question 56. Let there be an A.P. with first term a and common difference d. If an denotes its nth term and Sn is the sum of first n terms, then find:(vi) n and an, if a = 2, d = 8 and Sn = 90

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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  there be an A.P.

first term a and common difference d.

Also, If an denotes its nth term and Sn is the sum of first n terms,

Now we have to find n and an, if a = 2, d = 8 and Sn = 90

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 56(vi)

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1. Given A.P. has a=2, d=8 and Sn=90.

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

Sn = n[2a +(n – 1)d] / 2

So,

=> 90 = n[2(2) + (n – 1)8] / 2

=> 90 = n[2 + 4n – 4)]

=> 4n– 2n – 90 = 0

=> 4n– 20n + 18n – 90 = 0

=> 4n(n – 5) + 18n(n – 5) = 0

=> (n – 5) (4n + 18) = 0

=> n = 5 or n = –9/2

Ignoring n = –9/2 as n cannot be a fraction as well as negative. So, we get n = 5.

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

an = a + (n – 1)d

So,

= 2 + (5 – 1)8

= 2 + 32

= 34

Hence, the value of n is 5 and an is 34

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