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Chapter 4: Q. 44 (page 326)

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

Expert verified

The value of $a_{2} = 11$

Step by step solution

Step 1. Given information

Given sum:

\sum_{k = 3}^{10} a_{k} = 12 \sum_{k = 2}^{10} a_{k} = 23

Step 2. To find a2

$\sum_{k = 2}^{10} a_{k} = 23 a_{2} + \sum_{k = 3}^{10} a_{k} = 23 a_{2} + 12 = 23 a_{2} = 23 - 12 = 11$

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Find the sum or quantity without completely expanding or calculating any sums.Given∑k=310ak=12and∑k=210ak=23, finda2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. To find a2

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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 $a_{2}$ .