Question

write an expression for the 40th term of a geometric sequence whose first term is 5 and whose common ratio is 4.

Answer 1

The expression for the geometric sequence is $t_{40}$ = 5× $4^{39}$.

Geometric sequence:

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. $a_{n}$= a. $r^{n-1}$. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

Here we have to find an expression for the 40th term of the geometric sequence.

The first term is(a) = 5

Common ratio (r) = 4

Formula to find the nth term in the geometric sequence:

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

Now we have to find the 40th term of the sequence:

n = 40

a = 5

r = 4

$t_{40}$ = 5$4^{40 - 1}$

Therefore the expression is 5× $4^{39}$

To know more about the geometric sequence refer to the link given below:

https://brainly.com/question/24643676

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