Question

For an AP if sum of 51th term= 7650,find the 26 th term.

Answer 1

let in an AP , first term = a, common difference = d
Sn= n/2[2a+(n-1)d]---(1)

S51 = 51/2[2a+(51-1)d]
= 51/2[2a+50d]
=51/2* 2[a+25d]
=51[a+25d]----(2)
given
S51 = 7650

51[a+25d] =7650{from (2)}
a+25d =7650/51
a+25d= 150
a26= 150

Answer 2

let a is the first term and d is the common difference of AP

a/c to question ,
51/2 { 2a + (51 - 1)d} =7650
51 ( a +25d ) =7650
a +25 d =7650/51 =150 --------------(1)

now,
26th term = a + (26 -1)d
= a + 25 d
from equation (1)
26th = a+25 d =150 (answer)