Question 1113863: The first three consecutive terms of an exponential sequence are (x-1), 2x and (5x+3) respectively. 1.find the value of x. 2.find the common ratio. 3.find the sum of the first six terms.
Answer by greenestamps(13203)   (Show Source):
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The ratio between the second and first terms is the same as the ratio between the third and second terms:
 or 
Both values of x produce geometric sequences; but one of them is not very interesting:
x=3: 2, 6, 18, ...
x=-1: -2, -2, -2, ...
For x=3, the common ratio is 3, and the sum of the first 6 terms is 2+6+18+54+162+486 = 728.
Since we only needed to find the sum of the first 6 terms, it was easy simply to find the terms and add them. We could have used the formula for the sum of a finite geometric sequence. Since the formula is useful when we need to find the sum of a large number of terms, it is a useful formula to know.
where a is the first term and r is the common ratio.
For this problem,
The problem is not very interesting for the case where x=-1; in that case, the common ratio is 1, and the sum of the first 6 terms is 6(-2) = -12.
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