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Question
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
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Solution
a + b, a − b, a − 3b ... to 22 terms
\[\text { We have }: \]
\[\text { First term } = a + b, d = \left( a - b - a - b \right) = - 2b\]
\[n = 22\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ = \frac{22}{2}\left[ 2 \times (a + b) + (22 - 1)( - 2b) \right]\]
\[ = 11\left[ 2a - 40b \right] = 22a - 440b\]
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