Question

1. Find the sum of all numbers between 200 and 600 which are divisible by 7.

2. A farmer borrows Rs. 1,000 and agrees to repay with a total interest of Rs.140 in 12 instalments, each instalment is being less than the preceding instalment by Rs. 10. What should be his first instalment?
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Answer 1

Answer:

1. Numbers between 200 and 600 which are divisible by 16 are ( 208, 224, ...,592 )

First term (a) = 208

Common difference (d) = 16

Last term (l) = 592

Let the numbers between 200 and 600 which are divisible by 16 be n . Then

Using AP formula

l = a + (n – 1)d 592 =

208 + (n – 1)16 592 =

208 + 16n – 16 - %3D - 16n =

592 – 208+ 16 |3| - 16n =

592 – 192 - 16n 400 400 n =

16 n = 25

Let the sum of n numbers be Sn .Then

Using AP formula

Sum of the numbers between 200 and 600 which are divisible by 16 is 1000

2 . Since a farmer borrows Rs. 1000 and agrees to repay with a total interst of Rs. 140 12 instalments,

∴ we can conclude that,

Sn = 1000 + 140 = Rs. 1140 with n = 12

Since he is paying each instalment being less than the preceding instalment by Rs. 10,

∴ d = - 10.

Now, we need to find the first instalment,

i.e. a = ?

∴ the amount of first instalment should be Rs. 150