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The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 42 and the common ratio is 3/4. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

The population of a local species of dragonfly can be found using an infinite geometric series where a1 42 and the common ratio is 34 Write the sum in sigma not class=

Respuesta :

we are given

first term is

[tex] a_1=42 [/tex]

common ratio is

[tex] r=\frac{3}{4} [/tex]

now, we can find nth term

[tex] a_i=a_1(r)^{i-1} [/tex]

now, we can plug values

[tex] a_i=42(\frac{3}{4})^{i-1} [/tex]

now, we can write in sigma form

[tex] sum=\sum _{i=1}^{\infty }\:42(\frac{3}{4})^{i-1} [/tex]

now, we can find sum

we can use formula

[tex] sum=\frac{a}{1-r} [/tex]

now, we can plug values

we get

[tex] sum=\frac{42}{1-\frac{3}{4}} [/tex]

[tex] sum=168 [/tex]

so, option-D.................Answer

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