Question

for GP fifth term is 1875 and common ratio is 5 then first te rm is​

Answer 1

Step-by-step explanation:

Given:-

In the GP , fifth term is 1875 and the common ratio is 5

To find:-

Find the first term of the GP?

Solution:-

Common ratio of the given GP = (r)= 5

Fifth term of the GP = t5 = 1875

We know that

t1 is the first term and the common ratio is r then the general or nth term of a GP is tn = t1 ×(r)^(n-1)

t5 = t1 ×(5)^(5-1)

=>t5 = t1× (5)^4

=>t5 = t1 ×(625)

Fifth term = 625 × t1

According to the given problem

Fifth term of the given G P = 1875

=>625 × t1 = 1875

=>t1 = 1875/625

=>t1 = 3

First term = 3

Answer:-

The first term of the given GP = 3

Check:-

t1 = 3

r = 5

Fifth term = t1×r^4

=>t5 = (3)(5^4)

=>t5 = 3×625

=>t5 = 1875

Fifth term = 1875

Verified the given relation.

Used formula:-

• t1 is the first term and the common ratio is r then the general or nth term of a GP is tn = t1× (r)^(n-1)