Question

In an A.P 4th term is equal to 5 times of first term , 8th term is one more than twice the 4th term Find the arithmetic progression.

Answer 1

Answer:

The nth term of an A.P is given by

an=a1+(n−1)d

where d is the common difference

and  a1 is the first term of A.P

hence 4th term of an A.P is 

a4=a1+(4−1)d

⟹a4=a1+3d….eq(1)

given that 4th term of A.P is three times the first .

⟹a4=3a1

put value of a4 from eq(1)

⟹a1+3d=3a1

⟹3a1−a1=3d

⟹2a1=3d

⟹a1=23d….eq(2)

3rd term of A.P is given by

a3=a1+(3−1)d

a3=a1+2