Q4 of 67 Page 74

If an arithmetic progression’s first term is 2 and common difference 8 and sum of n terms is 90 then value of n will be:

Given, first term a = 2 and common difference d = 8 and Sn = 90.


Since the sum of n terms is
Sn =


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



90 =
⇒ 180 = n [4 + 8(n - 1)]
⇒ 180 = 4n + 8n(n – 1)
⇒ 180 = 4n + 8n2 – 8n
⇒ 180 = 8n2 – 4n
⇒ 45 = 2n2 – n
⇒ 2n2 – n – 45 = 0
⇒ n = 5, n = -4.5
Since, n is a number of terms, it cannot be negative.
∴ n = 5.

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