Find the number of terms

Algebra Level 2

13 + 28 + 43 + ⋯ + a n = 68210 \large 13 + 28 + 43 + \cdots + a_n = 68210

The n n terms being added on the left side of the above equation form an arithmetic progression in that order.

What is n ? n?


The answer is 95.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Use the formula s = n 2 [ 2 a 1 + ( n − 1 ) d ] s=\dfrac{n}{2}[2a_1 + (n-1)d]

68210 = n 2 [ 2 ( 13 ) + ( n − 1 ) ( 15 ) ] 68210 = \dfrac{n}{2}[2(13)+(n-1)(15)]

136420 = n ( 15 n + 11 ) 136420 = n(15n+11)

136420 = 15 n 2 + 11 n 136420 = 15n^2 + 11n

15 n 2 + 11 n − 136420 = 0 15n^2 + 11n - 136420 = 0

By using the quadratic formula, we get n = 95 n=95 .

18 Helpful 1 Interesting 2 Brilliant 6 Confused

I got stuck trying to solve the quadratic equation. What is the best way to go about this?

Thijs Hemme - 1 year, 6 months ago

It will end in a quadratic equation, since it is not factorable, use the quadratic formula.

A Former Brilliant Member - 1 year, 6 months ago

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