A sequence has an initial value of 10 and each term is twice the previous. Which function models this sequence?
1. [tex]a(n) = 10 \cdot 2^n[/tex]
2. [tex]a(n) = 10 \cdot 2^{n-1}[/tex]
3. [tex]a(n) = 10 + 2n[/tex]
4. [tex]a(n) = 10 + 2(n-1)[/tex]
Answer (2)
10 , 20 , 40 , 80 , ... a n = 2 ⋅ a n − 1 ⇒ q = 2 g eo m e t r i c se q u e n ce ⇒ a n = a 1 ⋅ q n − 1 a 1 = 10 an d q = 2 ⇒ a n = 10 ⋅ 2 n − 1 A n s . t hi s se q u e n ce m o d e l s : a n = 10 ⋅ 2 n − 1
The correct function modeling the sequence, which starts at 10 and doubles each term, is a ( n ) = 10 ⋅ 2 n − 1 . This matches the definition of a geometric sequence. Therefore, the answer is option 2.
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