Arithmetic Sequences, Maths Help! ?
Hey there, i need help with this arithmetic sequence, its really weird.
For the arithmetic sequence -5,2,9... find {n: Sn = 402 }
Anyone have any ideas?
The answer is:
{n:n = 12}
i just need the working out
Thanks so much :)
Update:i use tn instead of an, is there a difference?
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Verified answer
The formula is Sn = n(a1 + an)/2
and an = a1 + d(n-1)
so an = -5 + 7(n-1)
and 402 = n (-5 + -5 + 7(n-1) ) /2
multiply by 2, and do out: 804 = n (-10 + 7n - 7)
804 = n(-17 + 7n) = -17n + 7n^2
7n^2 - 17n - 804 = 0
(7n + 67)(n - 12) = 0
so n = 12 (it can't be -67/7)
--5, 2, 9, 16, 23, 30, .... find n if Sn = 402
we have (n/2){2(--5) + (n--1)(2 + 5)} = 402
Or n(7n -- 17) = 804 Or 7n^2 -- 17n -- 804 = 0 giving n = 12, -- 67/7
whence n = 12.
an=a1 +(n-1)d
an=-5 + (n-1)7 =7n -7 -5 =7n -12
Sn =n/2(a1 +an)
402 =n/2 (-5 +7n-12)
804 = n(7n-17)
804 =7n^2 -17n
7n^2 -17n -804 =0
(7n +67 )(n-12) =0
Disregarding negative answer, you get
n-12=0
n=12