Question

4.5, 9, 13.5, 18...

a. Is it Arithmetic or Geometric?
b. Find the next term
c. What is the common
difference/ratio?
d. Write the explicit formula
e. Calculate the 15th term​

Answer 1

a) Arithmetic

b) 22.5

c) 4.5

d) a_n = 4.5 + 4.5(n - 1)

e) a_15 = 67.5

Explanation:

a) Subtract one term by the term right before it, and the difference will be the common difference.

9 - 4.5 = 4.5

13.5 - 9 = 4.5

18 - 13.5 = 4.5

Therefore, the common difference is 4.5.

b) Since the common difference is 4.5, add 4.5 to the 18 (which was the last value given). The result is 22.5.

c) We have already figured out that the common difference is 4.5.

d) The explicit formula would be a_n = a1 + d(n - 1). The first term is 4.5 and d is also 4.5, so the explicit formula is a_n = 4.5 + 4.5(n-1).

e) Plug 15 into our explicit formula for n. a_15 = 4.5 + 4.5(14). The result is 67.5.

Answer 2

A. Arithmetic, because they have a common difference of 4.5

B. The next term will be 18 + 4.5 = 22.5

C. Common difference = T2 — T1 or T3 —T2

T2 — T1 = 9 — 4.5 = 4.5 or

T3 —T2 = 13.5 — 9 = 4.5

D. Tn = a + d( n — 1)

E. Tn = a + d( n — 1)

a = 4.5

d = 4.5

n = 15

T15 = 4.5 + 4.5( 15 — 1)

T15 = 4.5 + 4.5(14) = 67.5