Question

The fourth term of an arithmetic progression is 3. The sum of the fifth and seventh terms is -10. Find the common difference and the first term. Tq

Answer 1

4th term = a1 + 3d = 3
fifth + seventh term  = a1 +4d + a1 + 6d = -10

2a1 + 10d = -10
a1 + 5d = -5
a1 +  3d = 3   Subtract:-
2d = -8
d = -4   

so a1 - 12 = 3
a1 = 15

Answer:-   first term = 15 and common difference = -4