NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 27

Total: 106

If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.

Solution:

We have Sn = 3n2 + 5n, where Sn be the sum of n terms.
S1 = 3 × 1 + 5 × 1 = 3 + 5 = 8 = a1, S2 = 3 × 4 + 5 × 2 = 12 + 10 = 22 = a1+a2
⇒ 8 + a2 = 22 ⇒ a2 = 14
∴ d = a2–a1 = 14 – 8 = 6
Now, am = a + (m – 1)d ⇒ 164 = 8 + (m – 1) × 6
⇒

156

= m - 1 ⇒ m = 26 + 1 = 27

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