Answer:
The formula to the sequence
-5, 10/3, -20/9, 40/27, -80/81, ...
is
(-1)^n. 5×2^(n-1). 3^(1-n)
For n = 1, 2, 3, ...
Step-by-step explanation:
The sequence is
-5, 10/3, -20/9, 40/27, -80/81, ...
By inspection, we see the following
- The numbers are alternating between - and +
- The numerator of a number is twice the numerator of the preceding number. The first number is 5.
- The denominator of a number is 3 raised to the power of (1 minus the position of the number)
Using these, we can write a formula for the sequence.
(-1)^n for n = 1, 2, 3, ... takes care of the alternation between + and -
5×2^(n-1) for n = 1, 2, 3, ... takes care of the numerators 5, 10, 20, 40, ...
3^(1-n) for n = 1, 2, 3, ... takes care of the denominators 1, 3, 9, 27, ...
Combining these, we have the formula to be
(-1)^n. 5×2^(n-1). 3^(1-n)
For n = 1, 2, 3, ...
