Question

In an AP, if the common difference (d) = –4, and the seventh term (a₇) is 4, then find the first term.

Answer 1

n^th term of an AP is T_n=a+(n−1)d
For an AP with the first term as 'a' and common difference as 'd', the seventh term is a + 6d.
According to the question, the common difference(d) is −4 and the seventh term(a₇) is 4.
So, a + 6d will be
⇒ a + 6(−4) = 4
⇒ a = 28
Hence, the first term is 28.