Question

In a GP, second term is 12 and 6 term is 192 then first term is.........​

Answer 1

ANSWER -

Consider a G.P series where first term is 'a' and common difference is 'r'

Let the series be a, ar,ar^2,ar^3 and so on..

3rd term=12=ar^2

6th term=96=ar^5

Dividing ar^5/ar^2, we get r^3=8=2^3

Therefore r=2

And, a=3

The terms are: 3,6,12,24,48,96,192,384,768…. and so on

For finding the sum of the terms we use the formula, s=a*(1-r^n)/(1-r), where n is the number of terms

Therefore, s=3*(1–2^9)/(1–2)=1533

Answer 2

Answer:

The first term of GP is 6.

Step-by-step explanation:

• Sequence in which each preceding term is some constant multiple of previous term is called geometric progression.
• Let the geometric progression be a, ar, ar², ar³... upto n terms; where a is first term of GP and r is common ratio of GP.
• The n th term of GP is given by

$T(n) = a {r}^{n - 1}$

Given that :

• 2nd term of GP = 12
• 6 th term of GP = 192

Solution :

• Let, the first term of GP be a and common ratio be r.
• 2nd term of GP is ar = 12 -----(1)
• 6th term of GP is ar⁵ = 192 -----(2)
• Dividing equation (2) with equation (1), we get
• ar⁵/ar = 192/12
• ⇒r⁴ = 16
• ⇒r = 2.
• Hence, common ratio of GP is 2.
• Putting value of r in equation (1), we get;
• 2a = 12
• ⇒a = 6.
• Hence, first term of the given GP is 6.