Mathematics......Under number patterns-Geometric series If a question goes.determine the expression for the nth term of the following sequence if the a) 4th term is 24 and the 7th term is 192 in a geometric sequence.what formula do i use here?because i don't have the whole sequence?
Sj is not a "school subject" , label it Math to have the corresponding tutors look at it
So if this is a GS, then we are given:
ar^3 = 24 and ar^6 = 192
ar^6 / ar^3 = 192/24
r^3 = 8
r = 2
back in ar^3 = 24
8a = 24
a = 3
now you have a and r, and the whole world of geometric sequences is open to you.
Ok im sorry.When you say ar^3=24 what do u mean? And what does '^' mean?
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
To find the expression for the nth term of a geometric sequence, we need at least two terms from the sequence. In this case, knowing the 4th term and the 7th term is enough to find a solution.
A geometric sequence follows the pattern where each term is obtained by multiplying the previous term by a constant value called the common ratio (r).
Let's denote the first term of the sequence as "a" (a₁), and the common ratio as "r."
Given:
4th term (a₄) = 24
7th term (a₇) = 192
We can find the common ratio (r) using the formula:
r = (a₇ / a₄)
So in this case, the common ratio (r) would be:
r = 192 / 24 = 8
Now, we can determine the value of the first term (a₁) using the formula:
a₁ = a₄ / r³
Substituting the known values:
a₁ = 24 / (8³) = 24/512 = 3/64
Now we can determine the expression for the nth term of the sequence.
The general formula for the nth term of a geometric sequence is:
aₙ = a₁ * r^(n-1)
Substituting the values we found:
aₙ = (3/64) * 8^(n-1)
Therefore, the expression for the nth term of the given geometric sequence is (3/64) * 8^(n-1).