To solve this problem, we need to calculate the sum of the first four terms of the given geometric sequence. The sequence is defined as m,2m,4m,…, where each term is twice the previous term. The sum of the first four terms can be expressed as m+2m+4m+8m. We will calculate this sum and then determine which of the given options could not be the result of this sum.
The sequence is defined as m,2m,4m,8m. Each term is twice the previous term, and we need to find the sum of the first four terms.
The sum of the first four terms can be expressed mathematically as:
S=m+2m+4m+8m=15m
Since m is an integer, the possible sums for m=1,2,…,9 yield the following results:
- For m=1: S=15
- For m=2: S=30
- For m=3: S=45
- For m=4: S=60
- For m=5: S=75
- For m=6: S=90
- For m=7: S=105
- For m=8: S=120
- For m=9: S=135
Thus, the possible sums are 15,30,45,60,75,90,105,120,135.
To determine which of the given options could NOT be the sum of the first four terms, we compare the options against the calculated possible sums. Any option not in the list {15,30,45,60,75,90,105,120,135} is the answer.
The answer is the option that is not in the set of possible sums. If, for example, the option is 100, then it could not be the sum.
Thus, if 100 is among the options, we conclude:
100
(Replace 100 with the actual option that is not in the list if provided.)