Question

Find the value of √1 + 3 + 5 + 7+. . . . . . . . . . . . . . +101.​

Answer 1

51

if you see carefully, the given sequence is an arithmetic progression

hence, we can calculate the number of terms first using the nth term formula

101=a+(n-1)d

101=1+(n-1)2

100/2=(n-1)

the number of terms=51.

next,

sum of terms in an AP= n/2(a+l)

51/2(1+101)

we get 51x51

the root of 51² is 51

hence the answer is 51

hope it helps!