Write the sum using summation notation assuming the suggested pattern continues. -8-3+2+7+...+67

1 answer:

5 0

You can use the generic representation of a term of an arithmetic sequence:
$a_n=a_1+d(n-1)$
Filling in the values a₁=-8, d=5, you have
$a_n=-8+5(n-1)\\a_n=-13+5n$

Then the value of n for the last term can be found as
67 = -13 + 5n
80 = 5n
16 = n
and the sum can be written as

$S_{16}=\sum\limits_{n=1}^{16}{(-13+5n)}$

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