Question

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

Answer 1

Given: d = – 4, a₇ = 4

Step-wise calculation:

1. Use the nth-term formula of an A.P.:

a_n = a₁ + (n – 1)d

2. For n = 7:

a₇ = a₁ + 6d

3. Substitute values:

4 = a₁ + 6(–4)

= a₁ – 24

4. Solve: a₁ = 4 + 24

= 28

The first term a₁ = 28.