Find the sum of the arithmetic sequence 140, 134, 128…, if there are 33 terms

limfne2c 2022-10-17 Answered
Find the sum of the arithmetic sequence 140, 134, 128…, if there are 33 terms
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Answers (1)

Martha Dickson
Answered 2022-10-18 Author has 20 answers
We first work out the 33th term, the general formula for a sequence like this being a n = a 0 + n × d , d being the difference.
Every term is the previous plus or minus the differnce d=−6. So to get to the 33th term we take 32 of these steps (remember we call the first term a 0 and the 33th is thus a 32 -- remember this!!):
a 32 = 140 + 32 × ( - 6 ) = - 52
The sum is 33 × the average, or
= 33 × 140 + ( - 52 ) 2 = 33 × 88 2 = 1452
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