Geometric sequence is characterized by a common ratio
<u>(1) Sum of first 5 terms</u>
The first term of the sequence is:
The common ratio (r) is:
The sum of n terms is calculated using:
So, we have:
Hence, the sum of the first five terms is 93
<u>(2) Sum of first 5 terms</u>
The first term of the sequence is:
The common ratio (r) is:
The sum of n terms is calculated using:
So, we have:
Hence, the sum of the first five terms is 1694
<u>(3) Sum of first n terms</u>
The first term of the sequence is:
The common ratio (r) is:
The sum of n terms is calculated using:
So, we have:
Hence, the sum of the first n terms is
<u>(4) The first term</u>
The sum of the first 7th term of the sequence is:
The common ratio (r) is:
The sum of n terms is calculated using:
So, we have:
Multiply both sides by 4
Divide both sides by 2188
Rewrite as:
Hence, the first term is 1
<u>(5) Find the 7th term</u>
The first term of the sequence is:
The common ratio (r) is:
The nth term of a geometric sequence is:
So, we have:
Hence, the seventh term is 1458
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<u>(6) Sum of geometric sequence</u>
The first term of the sequence is:
The common ratio of the sequence is:
The number of terms is:
The sum of n terms is calculated using:
So, we have:
Hence, the sum of the first five terms is 242
<u>(7) The first term</u>
The sum of the first five terms is given as:
The common ratio is:
The sum of n terms is calculated using:
So, we have:
Solve for a
Hence, the first terms is 1
<u>(8) Sum to infinite</u>
The first term of the sequence is:
The common ratio (r) is:
The sum to infinite is:
So, we have:
Hence, the sum to infinite is 256
Read more about geometric sequence at:
brainly.com/question/18109692