# What is the sum of the arithmetic sequence 135, 123, 111 …, if there are 34 terms?

Feb 13, 2016

Sum of the sequence is $- 4284$.

#### Explanation:

We have to find the sum of arithmetic sequence {135, 123, 111 …} up to 34 terms.

In the sequence ${a}_{1} , {a}_{2} , {a}_{3} , \ldots . \ldots , {a}_{n}$ nth term is given by ${a}_{1} + \left(n - 1\right) d$ where ${a}_{1}$ is the first term $d$ is the constant difference (a_2-a_1). Here ${a}_{1}$ is $135$ and $d = - 12$, hence

${a}_{34} = 135 + 33 \cdot \left(- 12\right) = 135 - 396 = - 261$.

Sum of the series is given by $n \frac{{a}_{1} + {a}_{n}}{2}$ and in this case it turns out to be $34 \cdot \left(135 - 261\right)$ or $34 \cdot \left(- 126\right)$ or $- 4284$-