Question

2) Check whether the numbers . √2,√8, √18, √32. .......... are in A. P.? If it is
an A. P. then find s40​

Answer 1

√2,√8, √18, √32

d = √8 - √2

=> d = 2√2 - √2

=> d = √2

d = √18 - √8

=> d = 3√2 - 2√2

=> d = √2

d = √32 - √18

=> d = 4√2 - 3√2

=> d = √2

Since, the difference (d) is same

So, 2,√8, √18, √32 .......... are in A. P

Here, d = √2 ; a = √2

S40 = n/2 [2a + (n-1) d]

=> 40/2 [2(√2) + (40-1) √2]

=> 20 [2√2 + 39√2]

=> 20 × 41√2

=> 820√2