Question

Find the sum of first 25 term of the number whose nth term is an _ 3-2n

Answer 1

Answer:

Given:-

The nth term of an ap is 3 - 2n

To Find :-

The sum of first 25th term of an Ap

Solution:-

The nth term of Ap is 3 -2n

so , putting the value of n = 1 , 2, 3 .. we get,

a1 = 3 - 2 × 1 = 3 -2 = 1

a2 = 3 - 2 ×2 = 3 - 4 = -1

a3 = 3 - 2 ×3 = 3 - 6 = -3

so, a1 (1st term ) = 1

a2 ( 2nd term ) = -1

a3 ( 3rd term ) = -3

common difference (d) = a2 - a1 = -1 - 1 = -2

Now , sum of 25th term is ,

s25 = n/2 ( 2a + ( n -1 ) d)

s25 = 25/ 2 ( 2 × 1 +( 25 -1 ) -2 )

s25 = 25/2 ( 2 + 24 × {-2})

s25 = 25 /2 ( - 46 )

s25 = 25 × (-13)

s25 = 325

$\therefore{S25 = 325}$

★Note :-

• To find the sum of terms of an ap -

sn = $\frac{n}{2} × 2a + ( n-1) d$

• To find the number of terms in an ap-

an = a + ( n-1 ) d