Question

If for an A.P S51=7650,find the 26th term

Answer 1

Hi ,

Let a and d are first term and

common difference of an A.P

We know that ,

n the term of an A.P = an

an = a + ( n - 1 )d

a26 = a + ( 26 - 1 ) d

a26 = a + 25d ------( 1 )

Sum of n terms an A.P = Sn

Sn = n /2 [ 2a + ( n - 1 )d ]

S51 = 7650 ( given )

51/2 [ 2a + ( 51 - 1 )d ] = 7650

51 /2 [ 2a + 50d] = 7650

( 51 / 2 ) × 2 [ a + 25d ] = 7650

51 [ a + 25d ] = 7650

a + 25d = 7650 / 51

a + 25d = ( 51 × 150 ) / 51

a + 25d = 150

a26 = 150 [ from ( 1 ) ]

26 th term in given A.P = a26 = 150

I hope this helps you.

:)