Find the sum of the first n terms of the arithmetic sequence.−9 + (−12) + (−15)+ ... (to 10 terms)

CheemnCatelvew 2020-11-07 Answered

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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smallq9
Answered 2020-11-08 Author has 106 answers

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+(n1)d]
Sn=n/2[2(9)+(n1)(3)]
Sn=n2[183n+3]
Sn=n2[153n]
Sn=3n2[5+n]

Step 2 Given a=2 and a15=86 Consider, a15=86
a+(151)d=86[an=a+(n1)d]
2+14d=86
14d=84
d=6 Therefore the sum of the first 100 terms is, S100=1002[2(2)+(1001)(6)][Sn=n2[2a+(n1)d]]
=50(4+594)
=29900

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