Question

If \( a_n \) is the \( n \)th term of A.P. \( 3, 8, 13, 18, \dots \), then what is the value of \( a_{25} - a_{10} \)?

• A. \( 50 \)
• B. \( 75 \)
• C. \( 40 \)
• D. \( 55 \)

Hint:

The general formula for an arithmetic sequence is: \[ a_n = a + (n - 1)d. \]

Answer 1

The Correct Option is D

The general term of an arithmetic progression is given by:
\[ a_n = a + (n - 1)d. \] Here, \( a = 3 \) and \( d = 8 - 3 = 5 \). Finding \( a_{25} \):
\[ a_{25} = 3 + (25 - 1) \times 5 = 3 + 24 \times 5 = 3 + 120 = 123. \] Finding \( a_{10} \):
\[ a_{10} = 3 + (10 - 1) \times 5 = 3 + 9 \times 5 = 3 + 45 = 48. \] Now,
\[ a_{25} - a_{10} = 123 - 48 = 55. \]