Question

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.

Answer 1

a₄+a₈ = 37

a+3d+a+7d = 37
 
2a +10d = 37  ------------------------1

a₆+a₁₂ = 46

a+5d+a+11d = 46 

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

From 1 and 2

We get 
6d = 9
d= 3/2

Putting the value of d in  .1.

2a +10d = 37
2a + 10(3/2) = 37
2a + 15 = 37
2a = 22
a = 22/2
a = 11

Hence the first term is 11 with a common difference 3/2.

Answer 2

Answer:

The first term is 11

Step-by-step explanation:

a₄+a₈ = 37

a+3d+a+7d = 37

 

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

a₆+a₁₂ = 46

a+5d+a+11d = 46  

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

From 1 and 2

We get  

6d = 9

d= 3/2

Putting the value of d in  .1.

2a +10d = 37

2a + 10(3/2) = 37

2a + 15 = 37

2a = 22

a = 22/2

a = 11

Hence the first term is 11 with a common difference 3/2.