Respuesta :
The sum of the given geometric series is 2046.
What is a geometric sequence?
There are three parameters which differentiate between which geometric sequence we're talking about.
- The first parameter is the initial value of the sequence.
- The second parameter is the quantity by which we multiply the previous term to get the next term.
- The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is 'a'
and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)
Then the sequence would look like
[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]
(till the terms to which it is defined)
The function of the is given as [tex]\sum^5_{k=1}6(4)^{k-1}[/tex], therefore, the sum of the geometeric series can be written as,
Sum = 6 + 6(4¹) + 6(4²) + 6(4³) + 6(4)⁴
= 6[1 + 4¹ + 4² + 4³ + 4⁴]
= 6 [1+4+16+64+256]
= 2046
Hence, the sum of the given geometric series is 2046.
Learn more about Geometric Sequence:
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