Question

(7+14+21+28………..+700) is equal to

Answer 1

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Answer 2

Answer:

The series (7+14+21+28………..+700) is equal to 35350 .

Step-by-step explanation:

Formula  for airthmetic series

$a_{n}=a_{1}+ (n-1)d$

Sum of the airthmetic series is given by

$S_{n} = \frac{n(a_{1}+a_{n})}{2}$

Where n is the number of  terms $a_{1}$ is first term and $a_{n}$ is the nth term d is the common difference.

As given the series in the question be as follow .

7+14+21+28………..+700

Thus

$d=a_{2}-a_{1}$

Here

$a_{2}=14$

$a_{1}=7$

$a_{n}=700$

Thus d = 14 - 7

d = 7

Putting in the equation

$700=7+ (n-1)7$

700 = 7 + 7n - 7

700 = 7n

$n = \frac{700}{7}$

n = 100

Put in the equation

$S_{n} = \frac{100\times (7+700)}{2}$

$S_{n} = \frac{100\times (707)}{2}$

$S_{n} =50\times 707$

$S_{n} =35350$

Therefore the series (7+14+21+28………..+700) is equal to 35350 .