Question

(i) The 2nd term of a G.P. is 4 and the 4th term is 64; find its common ratio. G Find the 10th term and nth term of the G.P., 5, 25, 125,​

Answer 1

Answer:

Let a be the first term and r be the common ratio respectively. Then

Second term of G.P. is

ar=4. (from the question) …1

4^(th) term of G.P. is

ar^3=64 (from question) …2

Divide 2 by 1

ar^3/ar =64/4

r^2 =16

r=4

Answer 2

The required answers for the given question are, r = 4 , a_10 as 5^10 and an = 5^n

Given

• 2nd term of a G.P. is 4
• 4th term is 64
• G.P., 5, 25, 125,

To find

• common ratio
• 10th term and
• nth term

Solution

we are provided with the second term and for the term of a particular geometric progression and her asked to find the common ratio of the geometric progression.

ar = 4 and

ar^3 = 64

dividing both of the equations we get

r^2 = 16

or, r = 4

now we have to find the 10th the term and the nth term of a another geometric progression.

G.P., 5, 25, 125,

a = 5

r = 5

a_10 = ar^9

or, a_10 = 5 × 5^9

or, a_10 = 5^10

n th term ,

an = ar^(n-1)

or, an = 5 ×5^(n -1)

or, an = 5^n

therefore, the required answers for the given question are, r = 4 , a_10 as 5^10 and an = 5^n

#SPJ3