Question

a geometric sequence has an initial value of 25 and a common ratio of 1.8. Write a function to represent this sequence . Find.the 23rd term.

Answer 1

Use the formula

a_n = a_1•r^(n-1)

a_23 = 25•(1.8)^(23 - 1)

Can you finish?

Answer 2

23rd term of the given geometrical sequence is $a_{23} = 25(1.8)^{22}$.

Function to represent sequence is $25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}$

What is geometric sequence?

" Geometric sequence is defined as the sequence whose ratio of the consecutive terms is always constant."

Formula used

nth term of the geometric sequence

$a_{n} = a r^{n-1}$

a = first term

r = common ratio

$a_{n}$ = nth term

According to the question,

First term of the geometric sequence 'a' = 25

Common ratio of the geometric sequence 'r'  = 1.8

Substitute the value in the formula to get 23rd term,

$a_{23} = 25(1.8)^{23-1}$

⇒$a_{23} = 25(1.8)^{22}$

Function to represent this sequence

$a, a(r),a(r)^{2} , a (r)^{3} , ....... ,a(r)^{n}$

= $25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}$

Hence, 23rd term of the given geometrical sequence is $a_{23} = 25(1.8)^{22}$.

Function to represent sequence is $25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}$

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