NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 20

Total: 106

If the sum of a certain number of terms of the A.P. 25, 22, 19, .... is 116. Find the last term.

Solution:

Let a be the first term and d be the common difference.
We have a = 25, d = 22 – 25 = –3, Sn = 116
Since Sn =

[2a + (n - 1) d]
∴ 116 =

[50 + (n - 1) (- 3)]
⇒ 232 = 50n – 3n2 + 3n ⇒ 3n2 – 53n + 232 = 0
⇒ 3n2 – 24n – 29n + 232 = 0 ⇒ (3n – 29) (n – 8) = 0
⇒ n =

, 8
Since n ≠

as n can not be in the fraction form
∴ n = 8
Hence, the last term a8 = a + 7d = 25 + 7 (– 3) = 25 – 21 = 4.

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