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

Given:

• d = – 4

• a_{7 =} 4

To find: a (first term)

Now, in an AP we know,

a_n = a + (n – 1)d

Where, a_n is the n^th term in the AP, d is the common difference, and a is the first term in the AP

Putting values in the above equation for n = 7

a₇ = a + 6d

4 = a + 6( – 4)

a = 28

∴ The first term is 28