Question

2. Find the sum of the first 30 terms of an A.P. whose nth term is 3 2 + n.

Answer 1

Hi ,

It is given that ,

nth term of an A.P = an = 32 + n

a = a1 = 32 + 1 = 33

a2 = 32 + 2 = 34

a3 = 32 + 3 = 35
:
:
a30 = 32 + 30 = 62

First term ( a ) = 33 ,

Common difference ( d ) = a2 - a1

d = 34 - 33

d = 1

n = 30

last term = a30 = 62

Sum of n terms ( Sn ) = n/2[ a + an ]

S30 = ( 30/2 ) [ 33 + 62 ]

= 15 × 95

= 1425
Therefore ,

Sum of 30 terms in given A. P = 1425

I hope this helps you.

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