Find an explicit formula for a sequence of the form a1, a2, a3, with the initial terms given below. 0, − 1 2 , 2 3 , − 3 4 , 4 5 , − 5 6 , 6 7

t(n) = (-1)^n * n/(n+1)

Step-by-step explanation:

First thing I'd say is that, the denominator happens to always be 1 more than the numerator including the the first term, which is 0/1

For that, we'd say the numerator = n, and since the denominator is 1 more than, we say it is = n + 1.

Then again, there is an alternating negative sign, that comes after every 2 terms. Note that when n is odd, the terms happen to be negative, but then, when n is even, the terms are positive.

Take a look at (−1)n, the exact same thing happened, and thus, we multiply each term by (−1)n so as to get the alternating negative sign.

Ultimately, we say that each term is in the form of

t(n) = (-1)^n * n/(n+1), Where n ≥ 0

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

18

step-by-step explanation:

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