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:
Step-by-step explanation:
If the 4th lies opposite the 11th, then you know the 3rd lies opposite the 10th, the 2nd opposite the 9th, and the 1st opposite the 8th; meanwhile, in the reverse direction you'd find that the 5th lies opposite the 12th, the 6th opposite the 13th, and the 7th opposite the 14th. Move up one more bead and you're back at the 1st, which you already know lies opposite the 8th. Therefore there are 14 total bead
Answer:
12x^6y
Step-by-step explanation:
To find the 20th term in this sequence, we can simply keep on adding the common difference all the way until we get up to the 20th term.
The common difference is the number that we are adding or subtracting to reach the next term in the sequence.
Notice that the difference between 15 and 12 is 3.
In other words, 12 + 3 = 15.
That 3 that we are adding is our common difference.
So we know that our first term is 12.
Now we can continue the sequence.
12 ⇒ <em>1st term</em>
15 ⇒ <em>2nd term</em>
18 ⇒ <em>3rd term</em>
21 ⇒ <em>4th term</em>
24 ⇒ <em>5th term</em>
27 ⇒ <em>6th term</em>
30 ⇒ <em>7th term</em>
33 ⇒ <em>8th term</em>
36 ⇒ <em>9th term</em>
39 ⇒ <em>10th term</em>
42 ⇒ <em>11th term</em>
45 ⇒ <em>12th term</em>
48 ⇒ <em>13th term</em>
51 ⇒ <em>14th term</em>
54 ⇒ <em>15th term</em>
57 ⇒ <em>16th term</em>
60 ⇒ <em>17th term</em>
63 ⇒ <em>18th term</em>
66 ⇒ <em>19th term</em>
<u>69 ⇒ </u><u><em>20th term</em></u>
<u><em></em></u>
This means that the 20th term of this arithemtic sequence is 69.
Answer:
<u>The answer is option C. 6a-7</u>
Step-by-step explanation:
Given that
5(3a-1)-2(3a-2)=3(a+2)+v
Solve for v
∴ v = 5(3a-1)-2(3a-2) - 3(a+2)
∴ v = 15a - 5 - 6a + 4 - 3a - 6
∴ v = 15a - 6a - 3a - 5 + 4 - 6
∴ v = 6a - 7
<u>So the answer is option C. 6a-7</u>
