Question

find the sum of the following series 4,7,10......148

Answer 1

here is your answer
first we have to find n and then sn

Answer 2

An arithmetic progression is a series which has consecutive terms having a common difference between the terms as a constant value.

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

$AD=4, 7, 10....148$

$a=4\\d=13$

$n=?$

$a_n=148$

$a_n=a+(n-1)d$

$148=4+(n-1)3$

$148-4=3n-3$

$144+3=3n$

$147=3n$

$n=147/3$

$n=49$

$s_n=\frac{n}{2}[2a+(n-1)d]$

$s_{49}=\frac{49}{2}[2\times 4+(49-1)3$

$s_{49}=\frac{49}{2}[8+43\times 3]$

$s_{49}=\frac{49}{2}[8+ 144 ]$

$s_{49}=\frac{49}{2}\times 152$

$s_{49}=3724$

#SPJ2