Question

If \( a_n \) is the n-th term of the A.P. \( 5, 12, 19, \dots \), then what is the value of \( a_{40} - a_{35} \)?

• A. 20
• B. 35
• C. 30
• D. 55

Hint:

Use the formula \( a_n = a_1 + (n - 1) \cdot d \) to calculate any term in an A.P. and find differences between terms.

Answer 1

The Correct Option is C

The n-th term of an A.P. is given by the formula: \[ a_n = a_1 + (n - 1) \cdot d, \] where \( a_1 \) is the first term and \( d \) is the common difference. For the A.P. \( 5, 12, 19, \dots \), the first term is \( a_1 = 5 \) and the common difference is \( d = 12 - 5 = 7 \). Now, calculate \( a_{40} \) and \( a_{35} \): \[ a_{40} = 5 + (40 - 1) \cdot 7 = 5 + 39 \cdot 7 = 5 + 273 = 278, \] \[ a_{35} = 5 + (35 - 1) \cdot 7 = 5 + 34 \cdot 7 = 5 + 238 = 243. \] Thus: \[ a_{40} - a_{35} = 278 - 243 = 35. \] Thus, \( \boxed{35} \).