Question

the sum of nth terms of an ap is 3n^2+5n.find the ap and hence find its 16th term.

Answer 1

f = first term

d = common difference

The sum of first n terms of an AP is in the form of a second degree equation, i. e., an² + bn + c.

Here, a = d/2, b = f - (d/2) and c = 0.

In 3n² + 5n,

Co-efficient of n² = d/2 = 3.

∴ d = 3 × 2 = 6

6 is the common difference.

Co-efficient of n = f - (d/2) = 5

= f - 3 = 5

∴ f = 5 + 3 = 8

8 is the first term.

∴ The sequence is 8, 14, 20,......

16th term = f + 15d

= 8 + 15 × 6

= 8 + 90 = 98

98 is 16th term of the AP.

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