Geometric sequences help?
(5) The 2nd term of a geometric sequence is 7.
The 7th term is 224.
(a) Find an expression for the nth term of the sequence.
(b) Find the 15th term.
How do I figure out the common ratio and first term to answer this? Urgent, help please!
Best regards.
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If the second term is 7
Then the 3rd term is 7 x R (where R is the common ratio)
The 4th term is 7 x R^2
The 5th term is 7 x R^3
The 6th term is 7 x R^4
The 7th term is 7 x R^5
Therefore as we know that the 7th term = 224 it follows that
7R^5 = 224
Divide both sides by 7
R^5 = 32
As 2 x 2 x 2 x 2 x 2 = 32 it follows that the common ratio is 2
The first term is the second term divided by 2 = 7/2 = 3.5
The nth term = 7 x 2^(n-2) or if you want to express it in terms of the first term = 3.5 x 2^(n-1)
The 15th term = 7 x 2^(15 -2)
= 7 x 2^13
= 7 x 8192
= 57344