An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for Class 10 Question Number 4 Of Exercise 11 C For ICSE & CBSE Board Students.

Here you have to find the sum of first nth terms.

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# Find the sum ( 5+13+21+………+181)

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Given : The series 5+13+21+…+181.

Solution :

The given series 5+13+21+…+181 is in Arithmetic progression as there difference is same.

The first term in A.P is a=5

The common difference in the AP is d=13-5=21-13=8.

The last term is l=181.

The last term formula is,

l=a+(n-1)d

181=5+(n-1)8

176=(n-1)8

n-1=22

n=23

Now, The sum of the A.P series is

S_n=n/2[a+l]

Substitute the values,

S_{23}=23/2[5+181]

S_{23}=23/2 x 186

S_{23}=23 x 93

S_{23}=2139

Therefore, The sum of the series 5+13+21+…+181 is 2139