Question

a= 2 d= 8
$S_{n} = 90$
n=? an=?​

Answer 1

${\fbox{\boxed {\huge{\rm{\red{Answer}}}}}}$

Step-by-step explanation:

$\implies \: \large\mathbb{ S_{n} = \frac{n}{2} (2a + (n - 1)d)}$

$\implies \: \large\mathbb{ S_{n} = \frac{n}{2}( (2) + (n - 1)8)}$

$\implies \: \large\mathbb{90 = \frac{n}{2}(4 + 8n - 8)}$

$\implies \: \large\mathbb{90 = \frac{n}{2} (8n - 4)}$

$\implies \: \large\mathbb{90 = \frac{n}{ \cancel2} \times \cancel{4}(2n - 1) }$

$\implies \: \large\mathbb{ \frac{ \cancel{90}}{ \cancel{2}} = {2n}^{2} - n }$

$\implies \: \large\mathbb{45 = {2n}^{2} - n}$

$\implies \: \large\mathbb{ {2n}^{2} - n - 45 = 0}$

$\implies \: \large\mathbb{ \underline{{2n}^{2} - 10n} + \underline{9n - 45 }= 0}$

$\implies \: \large\mathbb{2n(n - 5) + 9(n - 5) = 0}$

$\implies \: \large\mathbb{(n - 5) \: \: (2n + 9) = 0}$

$\implies \: \large\fbox\mathbb{n = 5} \: \: \fbox \mathbb{n = \frac{- 9}{2} }$

$\large\bold{Here, \: n = \frac{ - 9}{2} \: \: is \: not \: possible .}$

$\large\mathtt{n = 5}$

$\implies \: \large \mathbb{ a_{n} = a + (n - 1)8}$

$\implies \: \large\mathbb{ a_{5} = 2 + (5 - 1)8}$

$\implies \: \large \mathbb{ = 2 + (4)8}$

$\implies \: = \large\mathbb{2 + 32}$

$\implies \: \large \fbox\bold{ a_{n} = 34}$

${\boxed{\huge{\red{\mathbb{BeBrainly...! }}}}}$

Answer 2

ANSWER:-

➣

• Given:-

$a= 2 \\ d= 8$

$S_{n} = 90$

$n=? \\ a&{n}=?$

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• SOLUTION:-

$\longrightarrow \: \large{ S_{n} = \frac{n}{2} (2a + (n - 1)d)}$

$\longrightarrow \: \large{ S_{n} = \frac{n}{2}( (2) + (n - 1)8)}$

$\longrightarrow \: \large{90 = \frac{n}{2}(4 + 8n - 8)}$

$\longrightarrow \: \large{90 = \frac{n}{2} (8n - 4)}$

$\longrightarrow \: \large{90 = \frac{n}{ \cancel2} \times \cancel{4}(2n - 1) }$

$\longrightarrow \: \large{ \frac{ \cancel{90}}{ \cancel{2}} = {2n}^{2} - n }$

$\longrightarrow \: \large{45 = {2n}^{2} - n}$

$\longrightarrow \: \large{ {2n}^{2} - n - 45 = 0}$

$\longrightarrow \: \large{ \underline{{2n}^{2} - 10n} + \underline{9n - 45 }= 0}$

$\longrightarrow \: \large{2n(n - 5) + 9(n - 5) = 0}$

$\longrightarrow \: \large{(n - 5) \: \: (2n + 9) = 0}$

$\implies \: \large \bf{n = 5} \: \: {n = \frac{- 9}{2} }$

•$\large \bf{n = \frac{ - 9}{2} \: \: is \: not \: possible .}$

Therefore,

$\large \bf{n = 5}$

$\longrightarrow \: \large { a_{n} = a + (n - 1)8}$

$\longrightarrow \: \large{ a_{5} = 2 + (5 - 1)8}$

$\longrightarrow \: \large { = 2 + (4)8}$

$\longrightarrow \: = \large{2 + 32}$

$\implies \: \large \bf{ a_{n} = 34}$

$\\ \\ Hence, \bf{a_{n}=34}$

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