Question

Find the sum or quantity without completely expanding or calculating any sums.

Given$\sum _{k=3}^{10}{a}_k=12$and$\sum _{k=2}^{10}{a}_k=23$, find$a_2$.

Short answer

The value of$a_2=11$

Step-by-step solution

Step 1. Given information

Given sum:

$$\begin{gathered} \sum _{k=3}^{10}{a}_k=12 \\ \sum _{k=2}^{10}{a}_k=23 \end{gathered}$$

Step 2. To find a2

$$\begin{gathered} \sum _{k=2}^{10}{a}_k=23 \\ {a}_2+\sum _{k=3}^{10}{a}_k=23 \\ {a}_2+12=23 \\ {a}_2=23-12 \\ =11 \end{gathered}$$