arithmetic progression A.P

Question

the fourth term of an arithmetic progression  A.P is 1 less than twice the second term. if the sixth term is 7. find the first term

Answer 1

In arthemetic sequence a n = a+(n-1)d

Here a is first term and d is common difference.

Given sixth term is a+5d = 7--------> (1)

And fourth term is 1 less than twice the second term ,we can also write it in equation form is be

2(a+d)-1 = a+3d

2a+2d-1 =a+3d

Bring all terms to one side.

2a+2d -1-a-3d = 0

a-d = 1 -------> (2)

To eliminate the a value subtract (2) from (1).

a+5d = 7

a - d  =  1

(-) (+)  (-) 

___________

6d = 6

Divide by 6 to each side.

6d/6 = 6/6

d = 1

Substitute the d value in (2)

a-1 = 1

Add 1 to each side.

a-1+1 = 1+1

a = 2

So the first term is 2.