Answer: 2685
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Explanation:
When we want to add up the first n terms of an arithmetic sequence, the formula to use is
S = (n/2)*( 2*a+d(n-1) )
where
S = sum of the first n terms
n = number of terms
a = first term
d = common difference
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In this case,
S = unknown
n = 30
a = -12
d = 7
which means,
S = (n/2)*( 2*a + d*(n-1) )
S = (30/2)*( 2*(-12) + 7*(30-1) )
S = 15*(-24 + 7*29)
S = 15*(-24 + 203)
S = 15*(179)
S = 2685
This answer is confirmed using a spreadsheet. Basically I had the spreadsheet generate 30 terms based on a pattern I gave it of the first two terms. Then I used the "SUM" function to add up all 30 terms quickly getting 2685.
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Side note:
Another formula we could use is
S = (n/2)*(a_1 + a_n)
where
a_1 = first term
a_n = nth term, when n = 30 this is the 30th term
The a_n part is equal to a_n = a_1 + d(n-1), and when you add this to the a_1 already in the S formula, that accounts for the 2*a_1 back in the first formula mentioned at the top of the page.
