First slide

Arithmetic progression

Question

The minimum number of terms of the series 1+ 3 + 9 + 27 + … so that the sum may exceed 1000, is

Moderate

A

7
B

5
C

3
D

None of these

Solution

Let, the sum of n terms exceeds 1000.
Then $\frac{1 (1 - 3^{n})}{1 - 3} > 1000; or \frac{3^{n} - 1}{2} > 1000$
$or 3^{n} > 2001; but 3^{6} = 729 and 3^{7} = 2187;$
$∴ n > 6$ ; but n is a positive integer
$∴ n = 7, 8, 9, \dots$
$∴$ The minimum number of terms = 7.

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