Question

1) Find the pattern and fill in the blanks. Determine if the sequence is arithmetic,

geometric, or neither. Then write the rule unless it is neither. Use t(n) format.
b. 64, 16, 4,
a. 5,8,11,14,.
Rule:
c. 7, 9, 13, 19,
Rule:
Rule:
d. 3, 18, 108,
Rule:

Answer 1

Explanation:

the picture does not fit to the text.

1.

a. 5, 8, 11, 14, 17

the rule here is clearly to add a constant 3 with the creation of a new term.

t(n) = 5 + 3(n - 1)

so, it is an arithmetic sequence.

b. 64, 16, 4, 1

the rule here is clearly to divide by a constant 4 (or multiply by 1/4) when a new term is created.

t(n) = 64/4^(n - 1)

so, it is a geometric sequence.

c. 7, 9, 13, 19, 27

the rule here is that there is a steadily increasing term added with the creation of a new term.

t(n) = t(n - 1) + (t(n - 1) - t(n - 2) + 2)

so, this is neither.

d. 3, 18, 108, 648

the rule is here to multiply by a constant 6 when a new term is created.

t(n) = 3 × 6^(n - 1)

so, this is a geometric sequence.

4.

she is using the ratio 8/3 for the new, larger amount.

for 3 dozen we get therefore 3×8/3 = 8 dozen.

so, she needs

16 × 8/3 = 128/3 = 42.666666666... ≈ 43 oz

of chocolate chips