Question

What is the sum of the first five terms of the geometric sequence in which a1=10 and r=1/2?

(Express your answer as an improper fraction using the slash (/) key and no spaces.)

Answer 1

the question is asking for an improper fraction

so it should be 155/8

Answer 2

Sum of first five terms is $19.3785$ OR in IMPROPER $\frac{155}{8}$.

What is a geometric sequence?

• When the ratio of consecutive terms of a sequence has a common ratio then it is a geometric sequence.
• In other words, each term is found by multiplying the previous term with a constant number called the common ratio.

How to find the common ratio of a geometric sequence

• As each term is found by multiplying the preceding term by the common ratio r, the common ratio can be found using the ratio of two consecutive terms which is

• $r= \frac{a_{n} }{a_{n} -1}$

Geometric series formula

• When the terms of a geometric sequence are added then it is called geometric series.

• If $a_{n} = a_{1} . r^{n-1} , r\neq 1$ than the sum of the first n terms of the sequence can be found using the formula

$S_{n} = a_{1} . (\frac{1-r^{n} }{1-r } )$

So according the question

Given :

First term $a1 = 10$

common ratio $r= 1/2$ $= 0.5$

number of term $n = 5$

Sum  of the first five terms $S_{n} = a_{1} . (\frac{1-r^{n} }{1-r } )$ ,

$S_{5} =\frac{10.(1 - 0.5^{5} )}{1 - 0.5}$ = $19.375$

Hence , the sum of the first five terms of the geometric sequence is $19.3785$ or in improper $\frac{155}{8}$.

Learn more about Geometric sequence on:

brainly.com/question/10714549

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