Question

Amit saves certain amount every month in a specific way. in the first month he saves rs 200, in the second month rs 250, in the third month rs 300 and so on. how much will be his total saving in 17 months?​

Answer 1

Answer:

Total amount saved in 17 months is Rs.10200

Step-by-step explanation:

Formula used:

The sum of n terms of an A.P a, a+d, a+2d,.... is

$S_n=\frac{n}{2}[2a+(n-1)d]$

Amount saved in 1st month = Rs.200

Amount saved in 2nd month = Rs.250

Amount saved in 3rd month = Rs.300

and so on

clearly 200, 250, 300,....... forms an A.P

Here, a=200 and d=50

Total Amount saved in 17 months

=Sum of the first 17 terms of the A.P

$=S_{17}\\\\=\frac{n}{2}[2a+(n-1)d]\\\\=\frac{17}{2}[2(200)+(17-1)(50)]\\\\=\frac{17}{2}[400+800]\\\\=\frac{17}{2}[1200]\\\\=17*600\\\\=Rs.10200$

Answer 2

Answer:

Rs 10200

Step-by-step explanation:

Amit saves certain amount every month in a specific way. in the first month he saves rs 200, in the second month rs 250, in the third month rs 300 and so on. how much will be his total saving in 17 months?​

First Month Saving = Rs 200

Second Month Saving = Rs 250

Third Month Saving = Rs 300

Second month - First Month = 250 - 200 = Rs 50

Third Month - Second Month = 300 - 250 = Rs 50

So Saving form an AP

where

a = first term = 200

d = common difference = 50

n = number of term = 17 months

Sum of n term = (n/2)(first term + nth Term)

nth Term = a + (n-1)d

Sum of n terms = (n/2) ( a + a + (n-1)d)

Savings for 17 months

Sum of 17 terms = (17/2)(200 + 200 + (17-1)*50)

= (17/2)(400 + 800)

= 17/2  * 1200

= 17 * 600

= 10200

Rs 10200