What is the sum of the first five terms of the geometric sequence in which

a1 = 3 and r= 1/3?

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

spaces.

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a1 = 3 and r= 1/3?

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

spaces.

121/27

Step-by-step explanation:

Precalc

To solve this problem you must apply the proccedure shown below:

1. You have that a1=6 and r=1/3, therefore you must apply the following formula:

Sn=a(1-r^n)/1-r

2. When you substitute the values shown above, you obtain:

S5=6(1-(1/3)^5)/(1-(1/3))

S5=242/27

Therefore, the answer is 242/27

121/27

Step-by-step explanation:

The sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is [tex]\frac{1}{2}[/tex] is [tex]19\frac{3}{8}[/tex]

Step-by-step explanation:

A geometric sequence is a sequence where each term is find by multiplying the previous term by a constant non-zero number known as the common ratio.

Here, given [tex]a_1=10[/tex] and [tex]r=\frac{1}{2}[/tex]

We have to find the sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is [tex]\frac{1}{2}[/tex].

Sum of a geometric sequence is given as :

[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]

Substitute the values,

[tex]S_n=\frac{10(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}[/tex]

Solving , we get

[tex]\Rightarrow S_n=\frac{10(1-(\frac{1}{2})^5)}{\frac{1}{2}}[/tex]

[tex]\Rightarrow S_n=\frac{10(1-\frac{1}{32})}{\frac{1}{2}}[/tex]

[tex]\Rightarrow S_n=\frac{10(\frac{32-1}{32})}{\frac{1}{2}}[/tex]

[tex]\Rightarrow S_n=\frac{10(\frac{32-1}{32})}{\frac{1}{2}}[/tex]

[tex]\Rightarrow S_n=20(\frac{31}{32})[/tex]

[tex]\Rightarrow S_n=10(\frac{31}{16})[/tex]

[tex]\Rightarrow S_n=\frac{310}{16}=\frac{155}{8}[/tex]

[tex]\Rightarrow S_n=19\frac{3}{8}[/tex]

Thus, the sum of the first five terms of the geometric sequence whose first term is 10 and common ratio is [tex]\frac{1}{2}[/tex] is [tex]19\frac{3}{8}[/tex]

(10(1-(1/2)^5)/1-(1/2) =

20(1-1/32)

=155/8

19.375

Step-by-step explanation:

a=10

r=1/2=0.5

Sn=a(1-r^n)/(1-r)

S5=10(1-(0.5)^5)/(1-0.5)

S5=10(1-0.03125)/(0.5)

S5=(10 x 0.96875)/(0.5)

S5=9.6875 ➗ 0.5

S5=19.375

1/4

Step-by-step explanation:

Sum of series of G.P. = Sn = a(1-rⁿ) / 1-r

Here, a = 5

r = 1/5

Substitute their values into the expression:

Sn = 5(1-1/5⁵) / 1 - 1/5

Sn = 5*5/4 [1-1/3125]

Sn = 25/4 [ 3124/3125]

Sn = 781 / 125

In short, Your Answer would be 781/125 in fraction form

or 6.248 in decimal form

Hope this helps!