Question

√2,√8,√18,√32,.....is an A. P.? If yes then what is sum of first 40 terms?​

Answer 1

Answer:

This is the only possible answer in decimal

Answer 2

Answer:

√2, √8, √18, √32

√2, √(2² × 2), √(3² × 2), √(4² × 2)

√2, 2√2, 3√2, 4√2,…..

For a series to be in AP, the common difference (d) should be Equal.

d1 = second term – first term = 2√2 – √2 = √2

d2 = Third term - Second term = 3√2 – 2√2 = √2

Since common difference is same the above series is in AP.

Sum of first 40 terms is = n/2[2a+(n-1)d]

= 40/2[2×√2+(40-1)√2]

= 20[2√2+39√2]

= 20[41√2]

= 820√2