First slide

Geometric progression

Question

$Consider the A.P a_{1}, a_{2}, a_{3} \dots a_{n}, the G.P b_{1}, b_{2} \dots b_{n} such that a_{1} = b_{1} = 1 : a_{9} = b_{9}$ $and \sum_{i = 1}^{9} a^{r} = 369 then$

Moderate

A

$b_{6} = 27$
B

$b_{7} = 27$
C

$b_{8} = 81$
D

$b_{9} = 18$

Solution

$a_{1} = b_{1} = 1, a_{9} = 1 + 8 d = b_{n} = 1 . r^{8}$
$\sum_{r = 1}^{9} a^{r} = \frac{9}{2} (1 + a_{9}) = \frac{9}{2} (1 + r^{8}) = 369$ $(s u m o f n t e r m s A . P = \frac{n}{2} (a + l))$
$\begin{array}{l} \Rightarrow r = \sqrt{3} \\ b_{7} = b_{1} r^{6} = 1 . (\sqrt{3})^{6} = 27 \end{array}$

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