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!