Question

Find the sum of the first 41 terms of the progression that begins: 32, 24, 16, …

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42 Answers

The given sequence is an arithmetic progression (AP) with a common difference of -8 (each term is obtained by subtracting 8 from the previous term).
In this case:
a = 32 (the first term),
d = -8 (the common difference), and
n = 41 (the number of terms).
Now, plug these values into the formula:
\[S_{41} = \frac{41}{2} [2(32) + (41-1)(-8)]\]
\[S_{41} = \frac{41}{2} [64 - 320]\]
\[S_{41} = \frac{41}{2} [-256]\]
\[S_{41} = -41 \times 128\]
\[S_{41} = -5248\]
Therefore, the sum of the first 41 terms of the given arithmetic progression is -5248.

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