Answer:
d(n) = 8n - 4
Explanations:
Let the initial number of dolls be represented by a
She began with 4 dolls
a = 4
Let the number of years be represented by n
The 24th years means that n = 24
She added the same amount of dolls to her collection each year
The common difference is d
The number of dolls in the 24th year is 196
d(24) = 196
This is an Arithmetic Progression (AP)
The nth term of an AP is given by the formula:
d(n) = a + (n - 1)d
d(24) = 4 + (24-1)d
196 = 4 + 23d
23d = 196 - 4
23d = 192
d = 192/23
d = 8.35 = 8 ( to the nearest whole number)
The function, d(n), that can be used to determine the number of dolls Vanessa had in any year
d(n) = a + (n-1)d
d(n) = 4 + (n-1)8
d(n) = 4 + 8n - 8
d(n) = 8n - 4