The sum of geometric sequence of 10 terms is 29,524
What is series?
A series in math is simply the sum of the various numbers or elements of the sequence. For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5 we will simply add them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
What is geometric sequence?
A geometric sequence is a sequence in which the ratio consecutive terms is constant.
An infinite series of the form a , ar , ar2 , ar3+⋯, where r is known as the common ratio and a is first term .
What is the geometric series?
A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.
An infinite series of the form a + ar + ar2 + ar3+⋯, where r is known as the common ratio and a is first term .
What Is the Geometric Sum Formula of finite terms?
[tex]Sn= \frac{a(r^{n}-1) }{r-1}[/tex]
Where
a is the first term
r is the common ratio
n is the number of terms
[tex]S_{n}[/tex] is sum of all the terms
According to question
1 + 3 + 9 + ................ 10th term
where
a = 1
r = 3/1 or 9/3 = 3 (common ratio )
n= 10
[tex]Sn= \frac{a(r^{n}-1) }{r-1}[/tex]
[tex]S_{10} = \frac{1(3^{10}-1) }{3-1}[/tex]
[tex]S_{10} = \frac{59049-1}{2}[/tex]
[tex]S_{10} = 29,524[/tex]
Hence , sum of geometric sequence of 10 terms is 29,524
To know more about geometric sequence here
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