Question

question evaluate the following sum. 1 + 4 + 7 +... + 40 select the correct answer below: 286 307 20 287 281

Explanation:

Step1: Identify the arithmetic - sequence

The sequence $1,4,7,\cdots,40$ is an arithmetic sequence with first term $a_1 = 1$ and common difference $d=3$.

Step2: Find the number of terms $n$

Use the formula for the $n$th term of an arithmetic sequence $a_n=a_1+(n - 1)d$. Substitute $a_n = 40$, $a_1=1$ and $d = 3$:
\[40=1+(n - 1)\times3\]
\[40-1=(n - 1)\times3\]
\[39=(n - 1)\times3\]
\[n-1=\frac{39}{3}=13\]
\[n = 14\]

Step3: Calculate the sum of the arithmetic sequence

Use the sum formula for an arithmetic sequence $S_n=\frac{n(a_1 + a_n)}{2}$. Substitute $n = 14$, $a_1=1$ and $a_n = 40$:
\[S_{14}=\frac{14\times(1 + 40)}{2}=7\times41=287\]

Answer:

A. 286