Question

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

Answer 1

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

Answer 2

Answer:

see explanation

Step-by-step 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 = $\frac{a_{2} }{a_{1} }$ = $\frac{100}{200}$ = $\frac{1}{2}$ , then

$a_{n}$ = 200 $(\frac{1}{2}) ^{n-1}$ ← explicit formula

The 15 th term is then

a₁₅ = 200 × $(\frac{1}{2}) ^{14}$

     = 200 × $\frac{1}{16384}$

     = $\frac{200}{16384}$ ← divide numerator/ denominator by 8

     = $\frac{25}{2048}$