Question

How do you find the sum of the arithmetic series `Sigma(7i-3)` from i=1 to 300?

Answer 1

In `sum (mx + b)`, the common difference of the series is `m` while the first term is `b`, if `i = 0` is the first term. Otherwise, just insert that value of `i` into the equation to find that term number. Using this technique, we find that `t_1 = 4`. There are `300 - 1 + 1 = 300` terms in this series.

`s_n = n/2(2a + (n - 1)d)`

`s_300 = 300/2(2(4) + (300 - 1)7)`

`s_300 = 150(8 + 2093)`

`s_300 = 315,150`

Hopefully this helps!