Question

sumit saves certain amount every month in a specific way. In the first month he saves rupees 200,in second month rupees 250,in 3rd month rupees 300 and so on. How much will his total savings be 17 months?​

Answer 1

Given :

• Amount Sumit saves in first month = Rs 200
• Amount Sumit saves in second month = Rs 250
• Amount Sumit saves in third month = Rs 300

To find :

Total amount saved by Sumit in 17 months

Formula used :

$\sf \bullet \: S_n\: = \: \bigg( \dfrac{n}{2} \bigg) \bigg( 2a \: + \: (n - 1)d\bigg)$

Here,

$\sf \bullet \: S_n\: = \: sum \: of \: n \: terms$

$\sf \bullet \: n \: = \: Number \: \: of \: terms \:$

$\sf \bullet \: a \: = \: First \: term \:$

$\sf \bullet \: d \: = \: Common \: difference$

Solution :

We can see that the amount saved by Sumit each month follow a A.P.

200 , 250 , 300 . . . and so on

Therefore,

• a = 200
• d = 250 - 200 = 50
• n = 17

$\sf \implies \: S_{17}\: = \: \bigg( \dfrac{17}{2} \bigg) \bigg( (2 \times 200) \: + \: (17 - 1) \times 50\bigg)$

$\sf \implies \: S_{17}\: = \: \bigg( \dfrac{17}{2} \bigg) \bigg( (400) \: + \: (16) \times 50\bigg)$

$\sf \implies \: S_{17}\: = \: \bigg( \dfrac{17}{2} \bigg) \bigg( 400\: + \: 800 \: \bigg)$

$\sf \implies \: S_{17}\: = \: \bigg( \dfrac{17}{2} \bigg) \bigg( 1200\: \bigg)$

$\sf \implies \: S_{17}\: = \: \bigg( 17 \times 600 \bigg)$

$\sf \implies \: S_{17}\: = \: 10200$

ANSWER : Rs 10,200