Name: Sum of First n Terms of an Arithmetic Progression
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: 13+13+13+13…….How do we find the sum of 50 terms of this series? Learn to find the sum of the first ‘n’ terms of an Arithmetic Progression with a real-life e...

Question

A man bought a scooter with

12

monthly instalments. He paid

₹ 6,000

as first instalment and thereafter for each instalment he paid

₹250

less than the previous month. By instalment if he paid

₹3150

extra over the original price, then find the original price of the scooter.

Accepted Answer

Given that a man bought a scooter with $12$ monthly instalments.

He paid $₹ 6,000$ as first instalment and thereafter for each instalment he paid $₹250$ less than the previous month.

Thus, we get a sequence of numbers in which the difference between each consecutive terms is $₹250$ .

Hence, this problem forms an A.P.

Let the first term of A.P $= a = ₹ 6,000$

Common difference $= d = ₹250$

Now, let us find the amount paid by a man at the end of the $12$ months.

We know that the sum of first $n$ terms of an A.P is given by

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

Thus,

$S_{12} = 6 [2 \times 6000 + 11 \times 250]$

$= 6 [12000 + 2750]$

$= 88, 500$

Thus, the amount pain by a man at the end of $12$ months is $₹ 88, 500$ .

It is given that he paid $₹3150$ extra over the original price.

Hence, the original price $₹250$

$= ₹ 85, 350$

A man bought a scooter with $12$ monthly instalments. He paid $₹ 6,000$ as first instalment and thereafter for each instalment he paid $₹250$ less than the previous month. By instalment if he paid $₹3150$ extra over the original price, then find the original price of the scooter.

Important Questions on Arithmetic Progressions

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