Question

The first term of G.P whose second term is 2 & sum of infinity will be ​

Answer 1

Step-by-step explanation:

$\blue{ \bf{ \underline{QUESTION} : - }}$

The first term of G.P whose second term is 2 & sum of infinity will be .

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$\boxed{ \bold{ \huge{ Given}}}$

• Second Term of G.P = 2

• $\bold{a_2 = 2}$

• $\bold{r = \frac{2}{a}}$

$\boxed{ \huge{ \bold{ to \: find}}}$

• Sum of infinity

$\star{ \pink{ \underline{ \underline{Ｓｏｌｕｔｉｏｎ : - }}}}$

${ \ \boxed{ \bold{ \purple{ \frac{a}{1 - r} =s _ \infty }}}}$

$\implies{ \bold{ \frac{ a} {1 - \frac{2}{a} } = s _ \infty}}$

$\implies{ \bold{ \frac{a}{ \frac{a - 2}{a} } = s_ \infty }}$

$\implies{ \bold{a \times \frac{a}{a - 2} = s _ \infty }}$

$\implies{ \bold{ \frac{ {a}^{2} }{a - 2} = s_ \infty }}$

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MORE YOU KNOW :➡️

• ${s_ n ={ \frac{a( {r}^{n} - 1) }{r - 1} { \sf{ \: if \: r > 1 \: and \:{ \: s_ n = \frac{a(1 - {r}^{n}) }{1 - r} if \: |r| < 1}}}}}$

• $\bold{a_n = a {r}^{n - 1}}$

• ${{ \bold{ { \frac{a}{1 - r} =s _ \infty }}}}$

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