Question

3) given a = 2, d-8, SE90, find n and an​

Answer 1

Answer:

a=2.

d-8 & d=8.

Sn=90.

to find n and an .

according to the formula: -->

an=a+(n-1)d .

an=2+(n-1)8.

an=>2+8n-8.

an=>-6+8n.........................i.

$sn = \frac{n}{2} (2a + (n - 1)d. \\ 90 \times 2 = n(2 \times 2 + (n - 1)8. \\ 180 = n(4 + 8n - 8). \\ 180 = > \: - 4n + 8 {n}^{2} \\ 8 {n}^{2} - 4n - 180. \\ 4(2 {n}^{2} - n - 45). \\ 2{n}^{2} - n - 45. \\ 2 {n}^{2} - 10n + 9n - 45. \\ 2n(n - 5) \: + 9(n - 5). \\ 2n + 9 = > \frac{ - 9}{2} .can \: not \: possible \: because \: it \: is \: in \: negative \: . \\ so \: n - 5 = 0. \\ n = 5.$

as putting in i

an=>-6+8(5).

an=> -6+40.

an => 34. & n=>5.

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