Answer:
7
Step-by-step explanation:
The first term is 2. The common ratio is -6/2 = -3. The n-th term is ...
an = a1·r^(n -1)
Using the last term value, we have ...
1458 = 2·(-3)^(n -1)
729 = (-3)^(n -1)
Taking logarithms, we have ...
log(729) = (n -1)·log(|-3|)
n = 1 +log(729)/log(3) = 1 +6 = 7
The series is 7 terms long.
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There are few enough terms that we can write them all out:
2 -6 +18 -54 +162 -486 +1458
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Additional comment
Had it worked out that n was computed to be an even number, we would have to declare "no solution."
