A sequence has an initial value of 10, and each term is twice the previous term. Which function models this sequence?

1) \(a(n) = 10 \times 2^n\)

2) \(a(n) = 10 \times 2^{n-1}\)

3) \(a(n) = 10 + 2n\)

4) \(a(n) = 10 + 2(n-1)\)

a ( 1 ) = 10 a ( 2 ) = 20 a ( 3 ) = 40
Lets look at available choices: * 1) ** a ( n ) = 10 ( 2 ) n a ( 1 ) = 10 ∗ 2 = 20 wrong as a(1) should be 10 2) a ( n ) = 10 ∗ 2 n − 1 is the right choice because if you put 1 as n in the first case you will get: [a(1)=10 2^{1-1}=10 2^{0}=10 1] 3) a ( n ) = 10 + 2 n a ( 1 ) = 10 + 2 = 12 wrong as a(1) should be 10 4) a ( n ) = 10 + 2 ( n − 1 ) a ( 1 ) = 10 right but... a ( 2 ) = 10 + 2 = 12 wrong as a(2) should be 20

and 4) can be dismissed, at once, because the is addition sign between them, and consecutive numbers should be multiplied.

In short 2) is the right answer

Answered by mackiemesser | 2024-06-10

The correct function that models the sequence starting from 10 and doubling each term is a ( n ) = 10 × 2 n − 1 . This function gives the initial term as 10 and allows subsequent terms to be double the previous terms. Thus, the answer is option 2.
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Answered by mackiemesser | 2024-12-23