Question

the sum of 5th and 7tterm of an a.p. is 52 and the 10th term is 46. find the a.p.

Answer 1

Let a be the first term and d be common difference,
Then the A.P. is a, a+d, a+2d

a5 + a7 = 52
a+4d + a+6d = 52
2a+10d =52

On taking 2 common
a+5d= 26 .......... 1️⃣

also, a10 = 46
a+ 9d= 46 .........2️⃣

Subtracting equation 1 from 2
d = 5 Then a= 1

Required A.P. is 1 , 6 , 11

Answer 2

a5 + a7=52............1
a+4d+a+6d=52
2a+10d=52
2(a+5d)=52
a+5d=52/2
a+5d=26.......1
a10=46
a+9d=46........2
sub 1 from 2
a+9d=46
a+5d=26
- - -
4d=20
d=5
put value of d in eq 1
a+25=26
a=1,d=5