What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Question

anonymous · Answer

183

anonymous · Answer

First, we find the common difference:
15 - 8 = 7
22 - 15 = 7
so the difference is 7 (d = 7)

We can plug this into the general equation for arithmetic sequence x = a + d(n - 1) where x is the value we're looking for, a is the first term, d is the difference, and n is the number term were looking for.

With this, the equation is x = 8 + 7(n-1), so the 26th term will be:
x = 8 + 7(26 - 1)
x = 8 + 7(25)
x = 183

Sum of an arithmetic series is the average of the first and last values times the number of terms:
average = (183 + 8) / 2 = 195.5
sum = 195.5 * 26 = 5083

anonymous · Answer

I suck at explaining but yeah... :P

anonymous · Answer

xD Good effort.