Answer:
A: an = 6n - 9
Step-by-step explanation:
third term in an arithmetic sequence is 9
a3 = a + 2d
a + 2d = 9
the fifth term is 21
a5 = a + 4d
a + 4d = 21
a + 2d = 9 (1)
a + 4d = 21 (2)
Subtract (1) from (2) to eliminate a
4d - 2d = 21 - 9
2d = 12
d = 12/2
d = 6
Substitute d = 6 into (1)
a + 2d = 9 (1)
a + 2(6) = 9
a + 12 = 9
a = 9 - 12
a = -3
nth term of this sequence = a + (n - 1)d
= -3 + (n - 1)6
= -3 + 6n - 6
= 6n - 9
an = 6n - 9
Since the bases are all 13, keep the base and add the powers.
13^(-11 + 16 + -3 + 4 + -5)
13^1 = 13
Am assuming the text of the problem is:
"At 6:00 p.m., the temperature was 55 Fahrenheit. At 11:00 p.m. that same evening, the temperature was 40 Fahrenheit. What real number represents the average change in temperature per hour?"
Average change in temperature per hour = (55 - 40)/(11 - 6)
Average change in temperature per hour = 15/5
Average change in temperature per hour = 3 Fahrenheit per hour
Answer is 33 remaining chocolate cupcakes and 22 remaining vanilla cupcakes.
