Find the 7th term of a Geometric progressions, if the first and the 5th term are 16 and A respectively
a=16
ar^4 = A
16r^4 = A
r^2 = √A/4
term(7) = a r^6
= a(r^4)(r^2)
= 16 (A/16)(√A/4)
= A^(3/2) / 4
testing:
suppose r = 3, then my first 7 terms are:
16, 48, 144, 432, 1296, 3888, 11644
According to my answer, term(7) = 1296^(3/2) / 4 = 46656/4 = 11664
dang! Go with ol' reliable mathhelper once again.
To find the 7th term of a geometric progression, we need to know the common ratio (r) of the progression. However, we are given the first term (a1) and the 5th term (a5) instead.
Given:
a1 = 16 (first term)
a5 = A (5th term)
To find the common ratio (r), we can use the formula for the nth term of a geometric progression:
an = a1 * r^(n-1)
For the 5th term:
a5 = a1 * r^(5-1)
A = 16 * r^4
Solving for r:
r^4 = A/16
Now, we are given that the 5th term (a5) is equal to A. Substituting this value, we have:
A = 16 * r^4
To find the 7th term, we can use the same formula for the nth term:
a7 = a1 * r^(7-1)
Substituting the given values:
a7 = 16 * r^6
Now, we know that r^4 = A/16, so we can substitute this value into the equation for the 7th term:
a7 = 16 * (A/16)^6
Simplifying:
a7 = A^6 / 16^5
Therefore, the 7th term of the geometric progression is A^6 / 16^5.
a = 16
r^4 = A
a_7 = a_5 * r^2 = 16√A