Question

find the sum of n terms of an ap√2;√8;√18;√32.....

Answer 1

A.P. = √2, √8, √18, √32

First term, a = √2

Second term, ${a_2}$ = √8 = 2√2

Common Difference, d = ${a_2}$ - a

d = 2√2 - √2 = √2

${a_n}$ = a + (n - 1)d

${a_n}$ = √2 + (n - 1)√2

${a_n}$ = √2 + √2n - √2 = √2n

Sum of n terms :-

${S_n}$ = n / 2 (a + ${a_n}$)

${S_n}$ = n / 2 (√2 + √2n)

${S_n}$ = n / 2 × √2(1 + n)

${S_n}$ = [√2n(1 + n)] / 2

Answer 2

hope this is the answer..