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Home » 18. The sum of and terms of an A.P. is and the sum of the and terms is Find the first term and the common difference of the A.P.
18. The sum of {{4}^{th}} and {{8}^{th}} terms of an A.P. is 24 and the sum of the {{6}^{th}} and {{10}^{th}} terms is 34. Find the first term and the common difference of the A.P.
Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma
18. The sum of {{4}^{th}} and {{8}^{th}} terms of an A.P. is 24 and the sum of the {{6}^{th}} and {{10}^{th}} terms is 34. Find the first term and the common difference of the A.P.

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solution:

Given, in an A.P

The sum of {{4}^{th}} and {{8}^{th}} terms of an A.P. is 24

⇒ {{a}_{4}}+{{a}_{8}}=24

And, we know that {{a}_{n}}=a+\left( n-1 \right)d

\left[ a+\left( 4-1 \right)d \right]+\left[ a+\left( 8-1 \right)d \right]=24

a+5d=12 …. \left( i \right)

Also given that,

the sum of the {{6}^{th}} and {{10}^{th}} terms is 34

⇒ {{a}_{6}}+{{a}_{10}}=34

\left[ a+5d \right]+\left[ a+9d \right]=34

a+7d=17 …… \left( ii \right)

Subtracting \left( i \right) form \left( ii \right), we have

a+7d-\left( a+5d \right)=17-12

2d=5

d=5/2

Using d in \left( i \right) we get,

a+5\left( 5/2 \right)=12

a=12-25/2

a=-1/2

Therefore, the first term is -1/2 and the common difference is 5/2.

i

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