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

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