Question

In an ap, if s5 + s7 = 167 and s10 = 235, then find the ap, where s n denotes the sum of its first n terms.

Answer 1

S5+s7=167
5/2{2a+(5-1)d} +7/2{2a+(7-1)}=167
10a+20d+14a+42d=167×2
24a+62d=167×2
divide by 2 both sides
12a+31d=167. ..........(1)
now
s10= 235
10/2{2a+9d}=235
5{2a+9d}=235
2a+9d=47. ..........(2)
multiply by 6 in equation. (2)
12a+54d=282. .........(3)
solving equation (1) and (3) ,we get
a=1 and d=5
ap. 1,6,11,16,21,26............

Answer 2

Answer:

S5+S7=5/2(2a+4d) +7/2(2a+6d)=167

=5a+10d+7a+21d=167

=12a+31d=167   [let this be eqn 1]

similarly,

from S10=235, we get 2a+9d=47 {let this be equation 2}

by solving eqn 1 and 2, we get a=1 and d=5

therefore the ap is 1,6,11........

Step-by-step explanation: