Question

The sum of the first 46 terms of the sequence 2, -1, -4,-7, …

Short answer

The sum of the first 46 terms of the sequence -3013

Step-by-step solution

Given Information 

Arithmetic sequence is 2, -1, -4,-7, …

Difference 

sequence 2, -1, -4,-7, …

first term is 2

difference is -2-2=-3

-4-(-1)=-3

d=-3

Sum formula

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ where{a}_{1}isthefirstterm \\ disthedifferencebetweentheterms \\ nisthenumberofterms \end{gathered}$$

Sum 

Substitute the values in sum formula

$$\begin{gathered} S_n=\frac{n}{2}\left(2a_1+(n-1)d\right) \\ n=46becauseweneedsumfor46terms \\ {S}_{46}=\frac{46}{2}\left(2\left(2\right)+(46-1)(-3)\right) \\ {S}_{46}=23\left(4+\left(45\right)(-3)\right) \\ {S}_{46}=23\left(4-135\right) \\ {S}_{46}=-3,013 \end{gathered}$$

The sum of the first 46 terms of the sequence -3013