Answer:
Step-by-step explanation:
The general term of a geometric sequence is ...
an = a1·r^(n-1)
You have the 2nd and 4th terms, so ...
a2 = a1·r^(2-1) = a1·r
a4 = a1·r^(4-1) = a1·r^3
We can find r from the ratio ...
a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9
Then r is ...
r = √(4/9) = 2/3 . . . . the common ratio
The first term is ...
a2 = 18 = a1·(2/3)
a1 = (3/2)·18 = 27
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The sum of the first 6 terms is ...
Sn = a1·(r^n -1)/(r -1)
S6 = 27·((2/3)^6 -1)/(2/3 -1)
S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9
The sum of the first 6 terms is 73 8/9.
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<em>Check on the sum</em>
The first 6 terms are ...
27, 18, 12, 8, 5 1/3, 3 5/9
Their sum is 73 8/9, as above.
