Sum solving

Algebra Level pending

The sum of a finite series can be calculated using the following formula.

$\displaystyle \sum_{a}^{n} d = na + \frac{dn(n-1)}{2}$

where $n$ is the number of terms, $d$ is the common difference and $a$ is the first term.

You are told that $n = 56$ , $d = 12$ and $\displaystyle\sum_{a}^{n} d = 296,016$

Find $a$

1 solution

Jack Rawlin
Jan 8, 2015

We already know three of the four values in the formula so inserting them should give us an easy solution.

$(296,016) = (56)a + \frac{(12)(56)((56) - 1)}{2}$

$296,016 = 56a + 18,480$

$277,536 = 56a$

$a = 4956$