Question

If \( a_n \) is an arithmetic sequence \( 5, 12, 19, ... \), then what is the value of \( a_{40} - a_{35} \)?

• A. \( 20 \)
• B. \( 35 \)
• C. \( 30 \)
• D. \( 55 \)

Hint:

The difference between two terms in an A.P. is given by: \[ a_m - a_n = (m-n) \cdot d. \]

Answer 1

The Correct Option is B

Given \( a = 5 \), \( d = 12 - 5 = 7 \). Using the formula:
\[ a_n = a + (n-1)d \] \[ a_{40} - a_{35} = [5 + (40-1) \cdot 7] - [5 + (35-1) \cdot 7] \] \[ = [5 + 273] - [5 + 238] \] \[ = 278 - 243 = \]