Mathematics: The 2nd term of an exponential sequence is 9 while the 4th term is 81.find the common ratio,the first term and the sum of the first five terms of the sequence

The 2nd term of an exponential sequence is 9 - id2912393882, gtjermaine3249

bunnyqueen124

05.05.2021

second term: 9

4th term:81

$(3rd \: term)^{2} = 9 \times 81$

=729

$\sqrt{729} = 27$

3rd term=27

${9}^{2} = a1x27 \\ 81 = 27a1$

a1=3 the first term

$81 = 3 \times {q}^{3}$

${q}^{3} = 27$

q=3

$s = 3x \frac{1 - {3}^{5} }{1 - 3} = 364.5$

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maisieisdabomb23

10.02.2022

1/3 or 0.333

Step-by-step explanation:

If we know that exactly 2 of the 6 rolls resulted in a 1. Then the number of ways to arrange the two 1s into 6 slots is

$C(6,2) = \frac{6!}{(6-2)!2!} = \frac{6*5}{2} = 15$ ways

Of these 15 ways, some of them have 1 at the 1 slot.

The number of ways to arrange the two 1s so that one 1 is in the 1st slot is 5. Because the 2nd 1 is in any of the other 5 slots.

Therefore, the probability that the first roll resulted in a 1,given that exactly two of the six rolls resulted in a 1 is

5 / 15 = 1/3 or 0.333

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