Find the sum of the first n terms of the arithmetic sequence.−9+(−12)+(−15)+... (to 10 terms) Find the sum of the first 100 terms of an arithmetic sequence with 15th term of 86 and first term of 2.
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Step 1 Given: −9+(−12)+(−15)+.... It is an arithmetic series with a=first term=−9
f=common difference=−12−(−9)=−3 Now sum of the first n terms is, Sn=n2[2a+(n−1)d]
Step 2 Given a=2 and a15=86 Consider, a15=86
⇒d=6 Therefore the sum of the first 100 terms is, S100=1002[2(2)+(100−1)(6)][∵Sn=n2[2a+(n−1)d]]
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