Respuesta :
Answer:
a) Fourth term of the progression is 24
b) Sixth term of the progression is 96
Step-by-step explanation:
Formula for geometric sequence is,
[tex]a_{n}=ar^{n-1}[/tex]
where [tex]a_{n}=n^{th} term\:of\:sequence[/tex]
a = first term of sequence
r = common ratio
Given that first term of GP is 3. So, a = 3. Also common ratio is 2. So, r = 2.
a) To find fourth term of progression that is, [tex]a_{4}[/tex].
Substituting the values in given formula,
[tex]a_{4}=3\left(2^{4-1}\right)[/tex]
Simplifying,
[tex]a_{4}=3\left(2^{3}\right)[/tex]
[tex]a_{4}=3\left(8\right)[/tex]
[tex]a_{4}=24[/tex]
Therefore, the fourth term of progression is 24
b) To find sixth term of progression that is, [tex]a_{6}[/tex].
Substituting the values in given formula,
[tex]a_{6}=3\left(2^{6-1}\right)[/tex]
Simplifying,
[tex]a_{6}=3\left(2^{5}\right)[/tex]
[tex]a_{6}=3\left(32\right)[/tex]
[tex]a_{6}=96[/tex]
Therefore, the sixth term of progression is 96
