Question

What is the 8th term of the geometric sequence a2 = 20 and r = 5

Answer 1

Answer:

8th term of geometric sequence is 312500

Step-by-step explanation:

 Given :  $a_2=20$ and common ratio (r) = 5

We have to find the 8th term of the geometric sequence whose $a_2=20$ and common ratio (r) = 5  

Geometric sequence is a sequence of numbers in which next term is found by multiplying by a constant called the common ratio (r).

     $a_n=ar^{n-1}$  ......(1)

where  $a_n$  is nth term and a is first term.

For given sequence

a can be find using  $a_2=20$ and r =  5

Substitute in (1) , we get,

$a_2=ar^{2-1}$

$\Rightarrow 20=a(5)$  

$\Rightarrow a=4$

Thus, 8th term of the sequence denoted as  $a_8$

Substitute n= 8 in (1) ,  we get,

$a_8=ar^{8-1} \\\\a_8=(4)r_{7} \\\\a_8=4(5)^7=4 \times 78125=312500$

Thus 8th term of geometric sequence is 312500