Question

Find the sum of arithmetic series 1+4+7…+52.

Answer 1

Step-by-step explanation:

1+4+7+10+13+16+19+21+24+27+30+33+36+39+42+45+48+52

Answer 2

Given series: $1+4+7+-----------+52$.

To Find: the sum of the arithmetic series.

Solution:

Understand that,

The series can be rewritten as: $1+4+7+10+13+16+19+21+24+27+30+33+36+39+42+45+48+52$

$a=1, d=3, l=52, n=18$

Find the sum of the given sequence.

$\[S = \frac{n}{2}\left[ {2a + \left( {n - 1} \right) \times d} \right]\]$

$\[\begin{array}{l} \Rightarrow S = \frac{{18}}{2}\left( {1 + 52} \right)\\ \Rightarrow S = 9 \times 53\\ \Rightarrow S = 477\end{array}\]$

Therefore, the sum of the given series is $477.$