Question

If r = 4 and ^a8 = 100, what is the first term of the geometric sequence?

Answer 1

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 :

⇒ $n_{th} term = ar^{n-1}$

⇒ $8_{th}term = a\times4^{8-1}$

⇒ $100 = a \times 4^{7}$

⇒ $100 = a \times 16384$

⇒ $a = \frac{100}{16384}$

⇒ a = 0.0061

Therefore, the first term of the geometric  sequence is 0.0061