Question on: JAMB Mathematics - 2022

To solve this problem, we need to find the common difference (d) of the arithmetic progression (AP) and then calculate the 4th term.

1. Find the common difference (d):
   The formula for the nth term of an AP is given by: a_n = a + (n - 1)d
   Where:
   • a_n is the nth term
   • a is the first term
   • n is the term number
   • d is the common difference
   
   We are given that the 10th term (a₁₀) is 32, and the first term (a) is 3/2. So, we can write:
   32 = 3/2 + (10 - 1)d
   32 = 3/2 + 9d
   9d = 32 - 3/2
   9d = 64/2 - 3/2
   9d = 61/2
   d = 61/18
2. Find the 4th term:
   Now we can find the 4th term (a₄) using the formula:
   a₄ = a + (4 - 1)d
   a₄ = 3/2 + 3 * (61/18)
   a₄ = 3/2 + 61/6
   a₄ = 9/6 + 61/6
   a₄ = 70/6
   a₄ = 35/3

Therefore, the 4th term of the AP is 35/3.