Question

If the sum of first n terms of an A.P is given by 3n2+5n, find the 20th term of the A.P.

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Answer 1

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Answer 2

Answer:

A.P. is 146.

Step-by-step explanation:

Given, sum of first n terms of an AP, Sn = 3n2 – n

Sn = 3n2 – n

Replacing n by n – 1, we get

Let the nth term of AP be an.

an=Sn-Sn-1

- 1)] an = (3n² –n) - [3(7 – 1)? – (n –

.. an

- 4, {n? – (n – 1°] -n + (n – 1) > an = 3

an = 3(n² – n² + 21 – 1) – 1 an = 3(2n – 1) - 1 = 6n – 4

Now,put n = 1 in an, we get a = 6×1−4 = 2put n = 2 in an, we get a2 = 6×2−4 = 8put n = 3 in an, we get a3 = 6×3−4 = 14and so on.So, required AP is, 2,8,14,.....

Putting n = 25, we get

a25 = 6 × 25 – 4 = 150 – 4 = 146

Thus, the 25th term of the given A.P. is 146.