Question

The sum of 5th term and 7th term of an A.P is 52 and the 10 th term is 46. Find A.P?​

Answer 1

6, 10, 14, 18....

See the attachment for full solution.

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Answer 2

Hello mate! Here is your answer.

According to the question, we are given that the sum of 5th term and 7th term of an A.P. is 52. This means that:

$\implies a_5+a_7 = 52$

$\implies a+(5-1)d+a+(7-1)d = 52$

$\implies a+4d+a+6d = 52$

$\implies 2a+10d = 52$

$\implies a+5d = 26 ---(1)$

Also, we are given that:

$\implies a_{10}=46$

$\implies a+(10-1)d=46$

$\implies a+9d=46 ---(2)$

On subtracting Equation (1) from (2), we get:

$\implies (a+9d)-(a+5d)=46-26$

$\implies a+9d-a-5d=20$

$\implies 4d=20$

$\implies d=5$

Substituting the value of d = 5 in Eq.(2):

$\implies a+9d = 46$

$\implies a+9 \times 5 = 46$

$\implies a+45 = 46$

$\implies a=1$

Hence, the values of 'a' and 'd' are 1 and 5 respectively.

We know that an A.P will be in the form of the following:

$= a,(a+d),(a+2d),(a+3d)...$

$= 1,(1+5),(1+10),(1+15)...$

$= 1,6,11,16...$

Hope it helps you!!!