Question

if a1+a2+a3+a4+a5=34 and a3.a5-53 what is a20?

Answer 1

a1 + a5 + a10 +a15 + a20 + a24  = 225        (given)

(a1+a24) + (a5+a20) + (a10+a15) = 225                                ....................1

let first term is a & common difference is d then

 a1 = a       ,  a24 = a+23d   ,       a1+a24 = 2a+23d             ...................2

 a5 = a+4d ,  a20 = a+19d ,         a5+a20 = 2a+23d           ...................3

 a10 = a+9d , a15 = a+14d ,        a10+a15 = 2a+23d            .....................4

putting 2 , 3 , 4 in eq 1 we get

3(2a+23d) = 225

2a+23d = 75                                                                          ....................5

now , a1 + a2 + a3 ............a24 = S24

 S24 = 24/2[2a+(24-10d) =12(2a+23d)                               .....................6

from 5 & 6

S24 = 12*75 = 900