Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({)1, 1/4, 1/16, 1/64, 1/256, ... text(})

Answer 1

Answer:

$T_n = \frac{1}{4^{n-1}}$

Step-by-step explanation:

Given

$({)1, 1/4, 1/16, 1/64, 1/256, ... (})$

Required

The general term

The given sequence is geometric.

So first, we calculate the common ratio (r)

$r = T_2/T_1$

So, we have:

$r = 1/4 \div 1$

$r = 1/4$

The function is then calculated using:

$T_n =T_1 * r^{n-1}$

This gives

$T_n =1 * 1/4^{n-1}$

$T_n = \frac{1}{4^{n-1}}$