Question

find the sum of series 7+10+13+16+19+22+25​

Answer 1

Answer:

here the 1st term a=7

common difference d=10-7=3

number of terms n= 7

so, sum of the series

=n/2{2a+(n-1).d}

=7/2{2.7+(7-1).3}

=7/2{14+6.3}

=7/2{14+18}

=7/2.32

=7.16

=112

Answer 2

The sum of the series = 112

Given :

The series 7 + 10 + 13 + 16 + 19 + 22 + 25

To find :

Sum of the series 7 + 10 + 13 + 16 + 19 + 22 + 25

Formula :

Sum of first n terms of an arithmetic progression

$\displaystyle \sf S_n= \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

Where First term = a

Common Difference = d

Solution :

Step 1 of 3 :

Write down the given series

Here the given series is 7 + 10 + 13 + 16 + 19 + 22 + 25

This is an arithmetic series

Step 2 of 3 :

Write down first term and common difference

First term = a = 7

Common Difference = d = 10 - 7 = 3

Step 3 of 3 :

Calculate sum of the series

Number of terms = n = 7

∴ The sum of the series

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

$\displaystyle \sf = \frac{7}{2} \bigg[(2 \times 7) + (7 - 1) \times 3 \bigg]$

$\displaystyle \sf = \frac{7}{2} \bigg[14 + 18 \bigg]$

$\displaystyle \sf = \frac{7}{2} \times 32$

$\displaystyle \sf = 7 \times 16$

$\displaystyle \sf = 112$

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