Answer:
Step-by-step explanation:
The standard form:
A, B and C are the integer.
We have:
Find the common denomintaor of given fractions.
We have 5, 4 and 2. The common denominator of 2, 4 and 5 is 20.
20 = 2 · 10 = 4 · 5 = 5 · 4
Thereofre multiply both sides by 20:
Answer:
3. 2
4. f(n) = 3 + 4(n - 1)
Step-by-step explanation:
3. The general term of the arithmetic sequence is given by:
A(n) = - 14 + (n - 1)(2)
To find the ninth term of this arithmetic sequence, just put in the general term.
∴ A(9) = - 14 + (9 - 1)(2) = - 14 + 8(2) = -14 + 16 = 2.
Therefore the ninth term in the arithmetic sequence is two.
4. To know which expression represents the given sequence, substitute different values for to conclude.
In Option A, f(n) = 4 + 3(n - 1). Substitute n = 1.
We get f(1) = 4 + 3(0) = 4. This is not the first term in the sequence and can be eliminated.
In Option B, f(n) = 4 + 3n. Substitute n = 1.
We get f(1) = 4 + 3(1) = 7, not 3 so can be eliminated.
Similarly in Option C, we get 7 and could be eliminated.
In Option D, f(n) = 3 + 4(n - 1). Substitute n = 1.
We get f(1) = 3 + 4(1 - 1) = 3, which is the first term in the sequence.
Similarly, f(2) = 3 + 4(2 - 1) = 3 + 4 = 7.
Substitute n = 3, 4 to get other terms as well.
So, we say f(n) = 3 + 4(n - 1) is the representation of the given arithmetic sequence.
