Question

If the 7th term of an A.P. is 4 and its common difference is 4, then what is its first term?

• A. 16
• B. 20
• C. 24
• D. 28

Hint:

Use the formula for the nth term to find the first term of an A.P. when other terms are given.

Answer 1

The Correct Option is B

The formula for the n-th term of an A.P. is: \[ a_n = a_1 + (n - 1) \cdot d. \] We are given: \[ a_7 = 4, \quad d = 4, \quad n = 7. \] Substitute into the formula: \[ 4 = a_1 + (7 - 1) \cdot 4 = a_1 + 6 \cdot 4 = a_1 + 24. \] Solving for \( a_1 \): \[ a_1 = 4 - 24 = -20. \] Thus, the first term is \( \boxed{-20} \).