Question

Find the denominator of the geometric progression {bn} if b1 = 5 and b5 = 80​

Answer 1

b

5

​

b

2

​

​

=

4

1

​

⇒

ar

4

ar

​

=

4

1

​

Where a is the first term & r is the common ratio.

⇒

r

3

1

​

=

4

1

​

⇒r

3

=4

⇒r=

3

4

​

=4

3

1

​

And,b

2

​

+b

5

​

=216

⇒ar+ar

4

=216

⇒ar(1+r

3

)=216

Replacing, r=4

3

1

​

⇒ar[1+(4

3

1

​

)

3

]=216

⇒ar[1+4]=216

⇒ar=

5

216

​

⇒a=

5r

216

​

=

5

3

4

​

216

​

∴ The first term is 5 34

​

216

​