Question

If the sum of first n terms of an A.P. is (1/2)(3n² + 7n), then find its nth term. Hence write its 20th term.

Answer 1

Answer:

62

Step-by-step explanation:

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Answer 2

The nth term of the A.P is equal to 5 + (n-1)×3.

The 20th term of the A.P is equal to 62.

Given that the sum of n terms of an A.P is equal to (1/2)(3n² + 7n) .

S1 (sum of the 1st term) = (1/2)(10) = 5 = a

S2(sum of 1st and 2nd term) = (1/2)(26) = 13 = a + a + d

=> 2a + d = 13

=> d = 13 - 10

=> d = 3

Common difference of the arithmetic progression is 3 and the first term is 5.

Nth term = 5 + (n-1)×3

The 20th term of the arithmetic progression= 5 + (20-1)×3

= 5 + 57

= 62