Question

i) given a = 4, d=2, S =-14, find n and a,

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Answer 1

Answer:

n = 7 and a = -8

Step-by-step explanation:

$given,\\ a_{n} =4 \\d=2\\S=-14 \\\\ a_{n}=a+(n-1)d \\ 4=a+(n-1)(2) \\4=a+2n-2\\a+2n=6\\a=6-2n \\\\ =>S=\frac{n}{2}[2a+(n-1)d] \\=> -14=\frac{n}{2}[2(6-2n)+(n-1)(2)]\\=> -14(2)=n[12-4n+2n-2]\\=>-28=n[10-2n] \\=>-28=10n-2n^{2} \\=>2n^{2}-10n-28=0 \\=>2(n^{2}-5n-14)=0 \\=>n^{2}-5n-14=0 \\=>n^{2}+2n-7n-14=0\\=>n(n+2)-7(n+2)=0 \\ =>(n+2)(n-7)=0 \\=>n=7,-2 \\\\ .'. \ n=7 \ [can't \ be \ negative] \\\\ .'. \ a=6-2(7)=6-14=-8$

Answer 2

Step-by-step explanation:

Given, a=4

S =-14

d= 2

n =?

Ans : I think there is a mistake in your given data