Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
Answer:
D-70
Step-by-step explanation:
It is a combination C(8,4)
Answer:
Output will be n+4 because :
when input is 1 output is 1+4=5
when input is 4 output is 4+4=8
when input is 5 output is 5+4 =9
so, when input is n output will be n+4
Answer: f(3)
Step-by-step explanation:
First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.
Implicitly differentiate the left side and take the derivative of the right side
Multiply both sides by 'y' which was defined as 2^x
Plug in x = 2 and x = 3 to see which slope is larger
