The first term of the geometric sequence is 0.0061
Step-by-step explanation:
The general form of geometric sequence is a, ar, ar²,ar³,.......
where,
- a is the first term of the sequence.
- r is the common ratio. Here, the common ratio r = 4.
- The 8th term of the sequence is 100. Hence n = 8.
The formula to find the nth term of the geometric sequence is given by :
⇒ [tex]n_{th} term = ar^{n-1}[/tex]
⇒ [tex]8_{th}term = a\times4^{8-1}[/tex]
⇒ [tex]100 = a \times 4^{7}[/tex]
⇒ [tex]100 = a \times 16384[/tex]
⇒ [tex]a = \frac{100}{16384}[/tex]
⇒ a = 0.0061
Therefore, the first term of the geometric sequence is 0.0061
