First & Last Terms

Algebra Level 1

If 18 18 numbers 54 , a 1 , a 2 , a 3 , … , a 16 , 14 54, a_1, a_2, a_3, \ldots, a_{16}, 14 form an arithmetic progression in this order, what is the value of a 1 + a 2 + a 3 + ⋯ + a 16 ? a_1+a_2+a_3+\cdots+a_{16}?

612 612 608 608 544 544 558 558

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Mahindra Jain by Mahindra Jain

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2 solutions

Sum of whole series = (n/2)( First term + Last term)= (18/2)( 54+14 ) = 612

Now the desired sum= 612- (54+14)= 544

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I also did it in the same way

Aman Bansal - 7 years, 2 months ago

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so what

Ajay Ramesh - 7 years, 2 months ago

it's saying sum a1 till a16, not sum of all series, this question give some missunderstanding,, -_-

Yodji Fufuri - 7 years, 2 months ago
Abdel Aziz Alfad
Mar 19, 2014

we just have to find the sum of all the terms then subtract (54+14) from it.

since there are 16 terms in between the first and last terms, there are 18 terms in all. using this, we have:

Sum= (18/2)*(54+14)

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