CPM Homework Help : PC3 Problem 12-10

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12-10.

Evaluate each the following sums.

$3+6+$ $9+\dots+90$
Steps (a):
Add the first and last terms.
Divide by $2$ .
Multiply by the number of terms.

$20+22+$ $24+\dots+100$
Hint (b):
How many terms are there?
Hint Answer (b):
$41$

$\displaystyle \sum _ { n = 1 } ^ { 41 } ( 2 n + 18 )$
Steps (c):
Add the first and last terms.
Divide by $2$ .
Multiply by the number of terms.

$\displaystyle \sum _ { k = 8 } ^ { 53 } ( 5 k - 3 )$
Hint (d):
How many terms are there? That is, if the sum started with $k = 1$ , what would it end with?
Hint Answer (d):
$46$

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