Question

The sum of the 1
st and 3
rd terms of an A.S is 20, and the sum of 2
nd and 4
th
terms is 26. What is an arithmetic Progression?

Answer 1

Given ,

The sum of 1st and 3rd term of AP is 20

So ,

$\sf \hookrightarrow{a + a + 2d = 20} \\ \\ \sf \hookrightarrow </p><p>2a + 2d = 20 \: - - - \: eq(i)$

and

The sum of 2nd and 4th term of AP is 26

So ,

$\sf \hookrightarrow a + d + a + 3d = 26</p><p> \\ \\ \sf \hookrightarrow2a + 4d = 26 \: - - - \: eq(ii)$

Subtract eq (i) from eq (ii) , we obtain

2a + 4d - (2a + 2d) = 26 - 20

4d - 2d = 6

2d = 6

d = 3

Put the value of d = 3 in eq (i) , we obtain

2a + 2(3) = 20

2a + 6 = 20

2a = 14

a = 7

Hence , the required AP is -

7 , 10 , 13 , 16 , .....