Question

a=2,d=8,sn=90,an=?n=?​

Answer 1

HEYA ❤️

YOUR ANSWER IS IN THE ATTACHMENT.

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Answer 2

${\red{\bf{\huge{Smile!}}}}$

${\bold{\underline{Given:-}}}$

a=2

d8

Sn=90

${\underline{\bold{Find:-}}}$

an=?

n=?

${\underline{\blue{\bold{solution:}}}}$

$sn = \frac{n}{2} (2a + (n - 1) \times d) \\ 90 = \frac{n}{2} (4 + 8n - 8) \\ 90 = \frac{n}{2} ( - 4 + 8n) \\ 90 = - 2n + 4 {n}^{2} \\ 4 {n}^{2} - 2n - 90 = 0$

Solving the quadratic equation:

$4 {n}^{2} - 20n + 18n - 90 = 0 \\ 4n(n - 5) + 18(n - 5) = 0$

here (n-5) is suitable for finding the value of n because n cannot be a fraction,

so,

$n = 5$

therefore the value of n is,

${\boxed{\bold{\green{5}}}}$

Finding an,

an=a+(n-1) d

an=2+4*8

an=34

therefore an is,

${\boxed{\bold{\green{34}}}}$

${\red{\bf{\huge{Thanks!}}}}$

Aami_21✨✨