the second term of a goemetric progression is 12 more than the first term.Find the third term of goemetric progression?
ratio is 12^n
if first term is 6, then second is 18, third is 6+144....
ar - a = 12 , (given)
a(r-1) = 12
a = 12/(r-1)
let r be any value except r = 1
e.g. let r = 2, then a = 12, terms are 12, 24 , 48, ....
let r = 3, then a = 6, terms are 6, 18, 54, ...
let r = 7, then a = 2, terms are 2, 14, 98, ....
let r = 3.5, then a = 4.8, terms are 4.8, 16.8, 58.8, ...
notice that each is a GP and the difference between the first two terms is 12
To find the third term of a geometric progression, we need to know the common ratio of the progression. However, in this case, we do not have the common ratio explicitly provided.
Let's assume that the first term of the geometric progression is "a" and the common ratio is "r".
Given that the second term is 12 more than the first term, we can write an equation: a * r = a + 12.
To determine the third term, we can use the fact that the third term of a geometric progression is found by multiplying the second term by the common ratio:
Third term = Second term * r = (a + 12) * r.
Since the value of the common ratio (r) is still unknown, we cannot determine the exact value of the third term with the given information. We need more information, such as another equation or another term in the progression, to solve for the values of "a" and "r", and then find the third term.