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


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 76793 by necxxx last updated on 30/Dec/19

$T h e s u m o f t h e f i r s t n t e r m s o f a s e r i e s$ $i s g i v e n b y : S_{n} = n^{2} + 7 n + 2 .$ $(i) F i n d a f o r m u l a f o r t h e n t h t e r m$ $(i i) w r i t e d o w n t h e f i r s t 5 t e r m s o f t h e$ $s e q u e n c e$
Commented by turbo msup by abdo last updated on 30/Dec/19

$\sum_{k = 0}^{n - 1} S_{k} = \sum_{k = 0}^{n - 1} (k^{2} + 7 k + 2)$ $= \sum_{k = 0}^{n - 1} k^{2} + 7 \sum_{k = 0}^{n - 1} k + 2 n$ $= \frac{(n - 1) (n - 1 + 1) (2 (n - 1) + 1)}{6}$ $+ 7 \frac{(n - 1) n}{2} + 2 n$ $= \frac{n (n - 1) (2 n - 1)}{6} + \frac{7}{2} n (n - 1) + 2 n$
Commented by necxxx last updated on 01/Jan/20

$t h a n k y o u s o s o m u c h . {I t}^{'} s c l e a r n o w$
	Answered by benjo 1/2 santuyy last updated on 30/Dec/19

	$(i) U n = S n - S n - 1 =$ $n^{2} + 7 n + 2 - {(n - 1)}^{2} - 7 (n - 1) - 2$ $= (2 n - 1) + 7 = 2 n + 6$
	Answered by Kunal12588 last updated on 30/Dec/19

	$T_{n} = S_{n} - S_{n - 1}$ $= n^{2} - {(n - 1)}^{2} + 7 n - 7 (n - 1) + 2 - 2$ $= 2 n - 1 + 7$ $= 2 n + 6 = 2 (n + 3) \forall n > 1$ $a s f o r n = 1$ $T_{1} = S_{1} = 10 [n o t S_{1} - S_{0}]$
	Commented by necxxx last updated on 01/Jan/20

	$T h a n k y o u$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum