Question

What's the sum of ten terms of a finite arithmetic series if the first term is 13 and the last term is 89?A) 490B) 510C) 520D) 500

Answer 1

We have an arithmetic series of 10 terms, where:

a1 = 13

a10 = 89

We know that an arithmetic series is defined by the recurrence equation:

an = a(n-1) + d = a1 + (n - 1)*d

Where d is a real number, and it is the parameter of the series. If we want to calculate the sum of the series, we can use the equation above:

We factor the terms:

= n( a1 + d(n - 1)/2 ) = n( 2a1 + d(n - 1) )/2

But an = a1 + d(n - 1), then:

Sum = n(a1 + an)/2

Using the information of the problem:

Sum = 10*(13 + 89)/2 = 5*102

Sum = 510

Answer: B