First slide

Arithmetic progression

Question

The sum of positive terms of the series $10 + 9 \frac{4}{7} + 9 \frac{1}{7} + \dots is$

Moderate

A

$\frac{352}{7}$
B

$\frac{437}{7}$
C

$\frac{852}{7}$
D

None of these

Solution

Here, $a = 10, d = - \frac{3}{7}$
Then $t_{n} = 10 + (n - 1) (- \frac{3}{7})$
t_n is positive if $10 + (n - 1) (- \frac{3}{7}) \geq 0$
$or 70 - 3 (n - 1) \geq 0 or 73 \geq 3 n; or 24 \frac{1}{3} \geq n$
$∴$ First 24 terms are positive.
$∴$ Sum of the positive terms
$\begin{array}{l} = S_{24} = \frac{24}{2} (2 \times 10 + 23 \times \frac{- 3}{7}) \\ = 12 (20 - \frac{69}{7}) = \frac{852}{7} \end{array}$

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