Question

#2: Given the geometric sequence 200, 100, 50, 25... (This one is tricky)

Write the explicit formula.
• Determine the 15th term of the sequence?

Answer 1

# 2: 200, 100, 50, 25 ... geometrik dizisi göz önüne alındığında (Bu biraz zor)
Açık formülü yazın.
• Dizinin 15. terimini belirleyin?

Answer 2

see explanation

Explanation:

The explicit formula for a geometric sequence is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 200 and r =
`(a_(2) )/(a_(1) )` =
`(100)/(200)` =
`(1)/(2)` , then

`a_(n)` = 200
`((1)/(2)) ^(n-1)` ← explicit formula

The 15 th term is then

a₁₅ = 200 ×
`((1)/(2)) ^(14)`

= 200 ×
`(1)/(16384)`

=
`(200)/(16384)` ← divide numerator/ denominator by 8

=
`(25)/(2048)`