Question

Find the 2nd term of an arithmetic sequence with t5 = 3 and t7 = 7?

Answer 1

Let a be the first term and d be the common difference

t5 = 3 = a + 4d
t7 = 7 = a + 6d

a + 6d - a - 4d = 7 - 3
2d = 4
d = 2

Sub d = 2,
3 = a + 4(2)
a = -5

t2 = a + d
t2 = -5 + 2
t2 = -3