3 7+9+11+13..., n = 10
Answer (1)
SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & n = 10 \\ & a_1 = 7 \\ & a_2 = 9 \\ & a_3 = 11 \\ \end{aligned}[/tex]Step 2: Find the common difference.[tex]\begin{aligned} d & = a_2 - a_1 = a_3 - a_2 \\ d & = 9 - 7 = 11 - 9 \\ d & = 2 = 2 \end{aligned}[/tex]Step 3: Solve for the sum of the terms of an arithmetic sequence.[tex]\begin{aligned} S & = \frac{n}{2}[2a_1 + (n - 1)d] \\ & = \frac{10}{2}[2(7) + (10 - 1)(2)] \\ & = 5[14 + (9)(2)] \\ & = 5(14 + 18) \\ & = 5(32) \\ & = \boxed{160} \end{aligned}[/tex]Hence, the sum of the first 10 terms of the sequence is 160.
