Question

the nth term of
AP is an= 2n+1 find it's sum​

Answer 1

nth term of the AP = 2n + 1

Thus,

It's first term = 2(1) + 1 = 3

Second term = 2(2) + 1 = 5

Third term = 2(3) + 1 = 7

and so on......

Thus, the AP is:

AP = 3, 5, 7, .........

Here, First term (a) = 3

Common Difference (d) = 5-3 = 2

Sum up to = n terms.

Hence,

Sum = n/2{2a + (n-1)d}

= n/2{2(3) + (n-1)2}

= n/2(6 + 2n - 2)

= n/2(4 + 2n)

= n(n + 2)

Hence, sum of the given AP is n(n+2).