SOLUTION: The second and seventh term of a GP are 18 and 4374 respectively. Find the first term

Question 1195934: The second and seventh term of a GP are 18 and 4374 respectively. Find the first term
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
geometric progression formula is An = a * r^(n-1)
when n = 2, the formula becomes A2 = a * r^1 = 18
when n = 7, the formula becomes A7 = a * r^6 = 4374
a is the first term in the progression.
solve for a in both terms 2 and 7 to get:
a = 18/r^1
a = 4374/r^6
since they both equal a, set the terms equal to each other to get:
18/r^1 = 4374/r^6
multiply both sides of the equation to r^6 and divide both sides of the equation by 18 to get:
r^6/r^1 = 4374/18
simplify the left side of the equation to get:
r^5 = 4374/18
take the fifth root of both sides of the equaion to get:
r = (4374/18)^(1/5)
solve for r to get:
r = 3.
when A2 = 18, the formula becomes:
18 = a * 3^1 = 18 = a * 3
divide both sides of the equation by 3 to get:
18/3 = a = 6.
when A7 = 4374, the formula becomes:
4374 = a * 3^6
solve for a to get:
a = 4374/3^6 = 6.
a is the first term in the formula which is equal to 6.
that's your solution.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The 7th term, 4374, is the 2nd term, 18, multiplied by the common ratio r 5 times:

The common ratio is 3.

The second term 18 is the first term times the common ratio:

ANSWER: The first term is 6

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