3. jessica is playing a board game with her mother. the spinner used for
the board game is broken up into 5 different colored pie shaped
pieces. in order to the win the game, jessica must try and get the
spinner to land on the color purple two times in a row. if she spins the
spinner twice, what is the probability that she will land on purple both
times?
oa.
1/100
ob
1/5
oc.
1/25
1/10
o d.
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C. 1/25

Step-by-step explanation:

I assume this is a fair spinner and the probability of landing in all colors is equal.

First spin:

p(purple) = 1/5

Second spin:

p(purple) = 1/5

The two spins are independent events, so the probability of landing on purple twice is the product of the two individual probabilities.

p(purple and purple) = 1/5 * 1/5 = 1/25

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for