Question

The 4^th and 10^th term of an A.P. are 13 and 25 respectively. Find its 24^th term.

Answer 1

Given: t₄ = 13, t₁₀ = 25.

Step-wise calculation:

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

Use t_n = a + (n – 1)d method of forming two linear equations and subtracting to eliminate a.

2. a + 3d = 13   ...(4^th term)

3. a + 9d = 25   ...(10^th term)

4. Subtract: (a + 9d) – (a + 3d) 

= 25 – 13

⇒ 6d = 12

⇒ d = 2

5. Substitute d into a + 3d = 13

⇒ a + 6 = 13

⇒ a = 7

6. 24^th term: a₂₄ = a + 23d

= 7 + 23 × 2 

= 7 + 46

= 53

The 24^th term is 53.