The sum of 4th and 8th terms of an A.P is 37 and the sum of 6th and 12th

terms is 46. Find the first term of the A.P.

sum of 4th and 8th term of the A.P. = 37

a₄ + a₈ =37

a + 3d + a + 7d = 37

2a + 10d = 37-------------(1)

and sum of 6th and 12th term = 46

a₆ + a₁₂ =46

a + 5d +a + 11d = 46

2a + 16d = 46----------------(2)

subtarcting (1) from (2),we get

2a + 16 d -(2a + 10d) = 46 - 37

2a + 16d - 2a - 10d = 9

6d = 9

d = 3/2

put the value of d= 3/2 in (1), we get

2a + 10 X 3/2 = 37

2a + 15 = 37

2a = 37 - 15

a = 22/2

a = 11

So, the first term os the A.P. is 11.

hope it will help you!!!!