Respuesta :
Formula for finding sum of terms in a geometric progression is:
Sn = a1 ( 1 - r^n) / (1 - r)
-61 = a1 (1 - -3^5 ) / ( 1 - - 3
-61 = a1 ( 1 - - 243 ) / 4
a1 = 4/ 244 * -61
a1 (The first term is therefore) = -1
The seventh term, a7, will be given by: an = a1 * r^n-1
a7 = -1 * ( -3 )^7-1
= -1 * (-3^6)
= - 729
Sn = a1 ( 1 - r^n) / (1 - r)
-61 = a1 (1 - -3^5 ) / ( 1 - - 3
-61 = a1 ( 1 - - 243 ) / 4
a1 = 4/ 244 * -61
a1 (The first term is therefore) = -1
The seventh term, a7, will be given by: an = a1 * r^n-1
a7 = -1 * ( -3 )^7-1
= -1 * (-3^6)
= - 729
The value of the seventh term of the series is -729.
Given-
The fifth term of the geometric series is -61.
The common ratio [tex]r[/tex] is -3.
We have to find out the seventh series of the given geometric series.
The formula for the nth term of the geometric series with initial value a and common ratio [tex]r[/tex] can be given as as,
[tex]a_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]
To find out the seventh term we need to find out the first term of the series. For this use the above formula and keep the value of fifth term to find out the value of first term. For fifth term the above formula can be given as,
[tex]a_5=\dfrac{a_1\times(-3)^5}{5-1}[/tex]
[tex]-61=\dfrac{a_1(1-(-243))}{4}[/tex]
Rewrite the equation for [tex]a[/tex]
[tex]a=\dfrac{-61\times 4}{244}[/tex]
[tex]a=-1[/tex]
Now the seventh term of the series is,
[tex]a_7=\dfrac{a_1\times(-3)^7}{7-1}[/tex]
[tex]a_7=\dfrac{(-1)\times(-3)^7}{6}[/tex]
[tex]a_7=-729[/tex]
Thus the value of the seventh term of the series is -729.
For more about the geometric series follow the link below-
https://brainly.com/question/1504226
