Question

What is the sum of the 40th and the 70th elements of the series defined as: \( s_n = s_{n-1} - 5, \; s_1 = 281 \)?

• A. 55
• B. 17
• C. 22
• D. 100
• E. 45

Hint:

For arithmetic sequences, use \(a_n = a + (n-1)d\) to find any term quickly.

Answer 1

The Correct Option is D

Step 1: General formula of arithmetic sequence.
Here, \(a = 281, d = -5\).
General term: \[ s_n = a + (n-1)d = 281 + (n-1)(-5). \] Step 2: Find \(s_{40}\).
\[ s_{40} = 281 + 39(-5) = 281 - 195 = 86. \] Step 3: Find \(s_{70}\).
\[ s_{70} = 281 + 69(-5) = 281 - 345 = -64. \] Step 4: Add.
\[ s_{40} + s_{70} = 86 + (-64) = 22. \] So the correct value is 22. Final Answer: \[ \boxed{22} \]