First slide

Arithmetico-Geometric Progression

Question

$The sum of the infinite number of terms of the series 1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \dots \dots . is k, then the the value of 16k is$

Moderate

A

31
B

33
C

34
D

35

Solution

$\begin{array}{l} \begin{matrix} S_{\infty} = \frac{a}{1 - r^{}} + \frac{d r}{{(1 - r)}^{2}} \\ H e r e a = 1, d = 3, r = \frac{1}{5} \end{matrix} \\ ∴ S_{\infty} = \frac{1}{1 - \frac{1}{5}} + \frac{3 \times \frac{1}{5}}{{(1 - \frac{1}{5})}^{2}} = \frac{5}{4} + \frac{15}{16} = \frac{35}{16} = k (g i v e n) \\ \Rightarrow 16 k = 35 \end{array}$

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