First slide

Arithmetic progression

Question

The value of $n$ for which $704 + \frac{1}{2} (704) + \frac{1}{4} (704) + \dots$ up $n$ terms $= 1984 - \frac{1}{2} (1984) + \frac{1}{4} (1984) - . . . .$ up to $n$ terms is

Moderate

A

5
B

3
C

4
D

10

Solution

According to the given condition
(704) $\{1 - \frac{1}{2^{n}}\} = \frac{(1984) (2)}{3} \{1 - \frac{(- 1)^{n}}{2^{n}}\}$ (2)
$\Rightarrow 128 = \frac{2112}{2^{n}} - 1984 \frac{(- 1)^{n}}{2^{n}}$
If $n$ is odd, we get $2^{n} = 32$ or $n = 5$
If $n$ is even, we get $128 = 128 / 2^{n} \Rightarrow n = 0 .$

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