Question

Analyzing Student Work Shanna writes the formula f(x + 1) = 2.5f(x) when f(1) = 2 to represent this sequence: 2, 5, 12.5, 31.25, … Which error did Shanna make? She used the incorrect common ratio. She used the incorrect initial value. She should have multiplied by f(x) rather then have it as an exponent. She treated the sequence as geometric instead of arithmetic.

Answer 1

the answer is . c) she should have multiplied by f(x) rather then have it as an exponent 

Answer 2

She should have multiplied by f(x) rather than have it as an exponent.

Explanation:

Here the given sequence,

2, 5, 12.5, 31.25,........

Since,

`(5)/(2)=(12.5)/(5)=(31.25)/(12.25)=2.5`

⇒The given sequence is a G.P. having the first term 2 and common ratio of 2.5,

If f(x) represents a term of this g.p. then f(x+1) will show the next term,

By the above sequence, Next term = 2.5 × Previous term,

⇒ f(x+1) = 2.5 × f(x)

Which is the formula represents the above sequence,

But, the formula written by her,

`f(x+1) = 2.5^(f(x))`

Hence, She should have multiplied by f(x) rather than have it as an exponent.