Q. 44 - Calculus

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 $a_2$.

Step-by-Step Solution

Answer

The value of  $a_2=11$

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 a 2

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