The nth term of a sequence is 3(n + 3). What are the first four terms?
12
15
1
18
21

What is the 50th term?

Which is the first term to be larger than 100?
The th term

see explanation

Step-by-step explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula

n = 1 : 3(1 + 3) = 3 × 4 = 12

n = 2 : 3(2 + 3) = 3 × 5 = 15

n = 3 : 3(3 + 3) = 3 × 6 = 18

n = 4 : 3(4 + 3) = 3 × 7 = 21

The first 4 terms are 12, 15, 18, 21

Substitute n = 50 into the n th term formula

n = 50 : 3(50 + 3) = 3 × 53 = 159 ← 50 th term

Equate n th term formula to 100, that is

3(n + 3) = 100

3n + 9 = 100 ( subtract 9 from both sides )

3n = 91 ( divide both sides by 3 )

n = 30.333...

Thus the first term to have a value larger than 100 is the 31 st term

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560