How do you find the sum of the arithmetic sequence 4+7+10+.....+22?

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Answer 1 · 2016-06-07T22:39:36

First, we need to find the number of terms. This can be done by using the formula $t_n = a + (n - 1)d$ , and solving for $n$ .

$t_n = a + (n - 1)d$

$22 = 4 + (n - 1)3$

$22 = 4 + 3n - 3$

$22 - 1 = 3n$

$21 = 3n$

$7 = n$

Now we can use the formula $s_n = n/2(a + t_n)$

$s_7 = 7/2(4 + 22)$

$s_7 = 7/2 xx 26$

$s_7 = 7 xx 13$

$s_7 = 91$

The sum of $4 + 7 + 10 + ... + 22$ is $91$

Hopefully this helps!