(1 point) For each of the following, decide if the given series is a geometric s
ID: 2887280 • Letter: #
Question
(1 point) For each of the following, decide if the given series is a geometric series. A. 5 +5x + 10x + 15x + 20x +.: Is this a geometric series? A. Yes B. No If this is a geometric series, enter the first term: and the ratio between successive terms: (Enter na for the first term and ratio if this is not a geometric series.) B. 5x 6r6 + 7x7 + 8x8 + .: Is this a geometric series? A. Yes B. No If this is a geometric series, enter the first term: and the ratio between successive terms: (Enter na for the first term and ratio if this is not a geometric series.) C. 15x+ 10x + 15x +20x + ...: Is this a geometric series? A. Yes B. NoExplanation / Answer
A. The series is
5 + 5x + 10x + 15x + ....
= 5 + (5x + (5x + 5) + (5x + 2*5) + .....)
The terms after the initial 5 form an arithmetic series.
Therefore, the answer is No.
The first term : na
The common ratio : na.
B. 5x5 + 6x6 + 7x7 + ....
The co-efficients are in A.P while the x terms are in G.P
Therefore, the answer is No.
The first term : na
The common ratio : na.
C. 1 + 5x + 10x + 15x + 20x + ....
Similar to A, the intial term has changed to 1.
The answer is No.
The first term : na
The common ratio : na.
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