Simple AP

Algebra Level 2

An arithmetic progression of n n terms has a first term 2 and common difference 4.

Given that the sum of all of this progression's terms is 1250, and
the sum of the first ( n − 1 ) (n-1) terms of this progression is 1152.

Find the value of n n .


The answer is 25.

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Ashish Menon by Ashish Menon , 20, India

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1 solution

Ashish Menon
May 27, 2016

When we subtract the sum of all terms from the sum of the first ( n − 1 ) (n - 1) th term of this progression, we get the nth term. Let a a be the first term, d d be the common difference, a n a_n be the nth term, S n S_n be the sum of all terms and S n − 1 S_{n - 1} be the sum of first ( n − 1 ) (n - 1) terms. S n − S n − 1 = a n 1250 − 1152 = a + ( n − 1 ) d 98 = 2 + ( n − 1 ) × 4 96 = ( n − 1 ) × 4 24 = n − 1 n = 25 S_n - S_{n - 1} = a_n\\ 1250 - 1152 = a + (n - 1)d\\ 98 = 2 + (n - 1)×4\\ 96 = (n - 1)×4\\ 24 = n - 1\\ n = \color{#69047E}{\boxed{25}}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Simple and nice

Hung Woei Neoh - 5 years ago

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Thanks! :) :)

Ashish Menon - 5 years ago

Did the same way.. Another approach can be using only Sn to find the value of n but it will be very tedious..

Sagar Shah - 5 years ago

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Yep. True.

Ashish Menon - 5 years ago

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