Respuesta :
Answer:
8th term of geometric sequence is 312500
Step-by-step explanation:
Given : [tex]a_2=20[/tex] and common ratio (r) = 5
We have to find the 8th term of the geometric sequence whose [tex]a_2=20[/tex] 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).
[tex]a_n=ar^{n-1}[/tex] ......(1)
where [tex]a_n[/tex] is nth term and a is first term.
For given sequence
a can be find using [tex]a_2=20[/tex] and r = 5
Substitute in (1) , we get,
[tex]a_2=ar^{2-1}[/tex]
[tex]\Rightarrow 20=a(5)[/tex]
[tex]\Rightarrow a=4[/tex]
Thus, 8th term of the sequence denoted as [tex]a_8[/tex]
Substitute n= 8 in (1) , we get,
[tex]a_8=ar^{8-1} \\\\a_8=(4)r_{7} \\\\a_8=4(5)^7=4 \times 78125=312500[/tex]
Thus 8th term of geometric sequence is 312500
