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
