The first term of an A.P is equal to thrice the common difference, what is the sixth term of the A.P, if the common difference is 8?

Analyze the question: We're told that in an arithmetic progression (A.P.), the first term equals three times the common difference, and the common difference is 8. We need the 6th term.

Concept: The nth term of an A.P. is Tₙ = a + (n − 1)d where a is the first term and d is the common difference.

Solution:

1. Common difference: d = 8
2. First term: a = 3d = 3 × 8 = 24
3. Sixth term: T₆ = a + (6 − 1)d T₆ = 24 + 5(8) T₆ = 24 + 40 T₆ = 64

Answer: The sixth term is 64, which is option A.

Tip: Always find the first term (a) before using the nth term formula. Here the wording "thrice the common difference" simply means a = 3d. Watch out for option D (24), which is just the first term, a common trap if you stop too early!