"Let ${a_1}$ , ${a_2}$ , ${a_3}$ ,....... be a G.P. such that ${a_1}$

Question

"Let ${a_1}$ , ${a_2}$ , ${a_3}$ ,....... be a G.P. such that ${a_1}$ < 0, ${a_1}$ + ${a_2}$ = 4 and ${a_3}$ + ${a_4}$ = 16. If $\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda$, then $\lambda$ is equal to:"

Accepted Answer

"${a_1}$ + ${a_2}$ = 4

$\Rightarrow$ ${a_1}$ + ${a_1}$r = 4 ...(1)

${a_3}$ + ${a_4}$ = 16

$\Rightarrow$ ${a_1}$r² + ${a_1}$r³ = 16 ...(2)

Doing (1) $\div$ (2), we get

r = $\pm$ 2

If r = 2, then a₁ = ${4 \over 3}$

If r = -2, then a₁ = -4

Given ${a_1}$ < 0

$\therefore$ a₁ = -4

$\therefore$ $\sum\limits_{i = 1}^9 {{a_i}}$ = ${{a\left( {{r^9} - 1} \right)} \over {r - 1}}$ = 4$\lambda$

$\Rightarrow$ ${{ - 4\left( {{{\left( { - 2} \right)}^9} - 1} \right)} \over { - 2 - 1}}$ = 4$\lambda$

$\Rightarrow$ $\lambda$ = -171"

Let ${a_1}$ , ${a_2}$ , ${a_3}$ ,....... be a G.P. such that
${a_1}$ < 0, ${a_1}$ + ${a_2}$ = 4 and ${a_3}$ + ${a_4}$ = 16.
If $\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda$, then $\lambda$ is equal to:

Solution

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Let ${a_1}$ , ${a_2}$ , ${a_3}$ ,....... be a G.P. such that ${a_1}$ < 0, ${a_1}$ + ${a_2}$ = 4 and ${a_3}$ + ${a_4}$ = 16. If $\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda$, then $\lambda$ is equal to:

Solution

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Drill 25 more like these. Every day. Free.

Let ${a_1}$ , ${a_2}$ , ${a_3}$ ,....... be a G.P. such that
${a_1}$ < 0, ${a_1}$ + ${a_2}$ = 4 and ${a_3}$ + ${a_4}$ = 16.
If $\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda$, then $\lambda$ is equal to: