Question

How many terms of the A.P 25, 22, 19............... must be taken to give a sum of 116? Also find the last term

Answer 1

use formula
Sn=n/2 {2a+(n-1) d}
where a is first term and d is common difference.
116=n/2 {2 x 25+ (n-1)(-3)}

232=n (50-3n+3)

232=53n-3n^2

3n^2-53n+232=0

use quadratic formula

n=8,58/6
but n=58/6 isn't possible
hence n=8

last term
t8=a+7d=25-21=4

Answer 2

last term of series is 4.
number of terms is 8
.