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

Find the sum of the arithmetic sequence 140, 134, 128…, if there are 33 terms
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Martha Dickson
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!!):
${a}_{32}=140+32×\left(-6\right)=-52$
The sum is $33×$ the average, or
$\sum =33×\frac{140+\left(-52\right)}{2}=33×\frac{88}{2}=1452$
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