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The-sum-of-the-first-n-terms-of-a-series-is-given-by-S-n-n-2-7n-2-i-Find-a-formula-for-the-nth-term-ii-write-down-the-first-5-terms-of-the-sequence-

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Question Number 76793 by necxxx last updated on 30/Dec/19
The sum of the first n terms of a series is given by: S_n =n^2 +7n+2. (i)Find a formula for the nth term (ii)write down the first 5 terms of the sequence
Thesumofthefirstntermsofaseriesisgivenby:Sn=n2+7n+2.(i)Findaformulaforthenthterm(ii)writedownthefirst5termsofthesequence
Commented by turbo msup by abdo last updated on 30/Dec/19
Σ_(k=0) ^(n−1) S_k =Σ_(k=0) ^(n−1) (k^2 +7k+2) =Σ_(k=0) ^(n−1) k^2 +7Σ_(k=0) ^(n−1) k +2n =(((n−1)(n−1+1)(2(n−1)+1))/6) +7 (((n−1)n)/2) +2n =((n(n−1)(2n−1))/6) +(7/2)n(n−1) +2n
∑k=0n−1Sk=∑k=0n−1(k2+7k+2)=∑k=0n−1k2+7∑k=0n−1k+2n=(n−1)(n−1+1)(2(n−1)+1)6+7(n−1)n2+2n=n(n−1)(2n−1)6+72n(n−1)+2n
Commented by necxxx last updated on 01/Jan/20
thank you so so much.It′s clear now
thankyousosomuch.It′sclearnow
Answered by benjo 1/2 santuyy last updated on 30/Dec/19
(i) Un = Sn − Sn−1= n^2 +7n+2 −(n−1)^2 −7(n−1)−2 =(2n−1)+7=2n + 6
(i)Un=Sn−Sn−1=n2+7n+2−(n−1)2−7(n−1)−2=(2n−1)+7=2n+6
Answered by Kunal12588 last updated on 30/Dec/19
T_n =S_n −S_(n−1) =n^2 −(n−1)^2 +7n−7(n−1)+2−2 =2n−1+7 =2n+6=2(n+3) ∀ n>1 as for n=1 T_1 =S_1 =10 [not S_1 −S_0 ]
Tn=Sn−Sn−1=n2−(n−1)2+7n−7(n−1)+2−2=2n−1+7=2n+6=2(n+3)∀n>1asforn=1T1=S1=10[notS1−S0]
Commented by necxxx last updated on 01/Jan/20
Thank you
Thankyou

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