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:
6/9 = 2/3
Step-by-step explanation:
1/3 = 3/9
3/9 = 3/9
3/9 + 3/9= 6/9 = 2/3
Answer:
B
Step-by-step explanation:
The best - well, only way- is to check a few points.
Namely -1 (unless your eyesight is really poor!), 0, 1, 2, and 3.
Now you can mark all these points in each graph (well, you could if they were on paper and not on a screen) and see which one of the lines passes through all of them. Spoiler alert, it's the B graph.
A represents 
, B is the one you want, C is 
and D looks like 
Answer:
-210
Step-by-step explanation:
11n+12- combined like terms
