What is the 10th term of the progression -8,4,-2?
Thank you
Oh, the 10th term of that progression is the best at playing hide and seek. It doesn't want to be found! But don't worry, I'll tell you where it's hiding.
To find the 10th term, we need to figure out the pattern. From -8 to 4, we're multiplying by -0.5. And from 4 to -2, we're multiplying by -0.5 again. So, it seems like this sneaky progression is playing a game of "Multiply by -0.5"!
Now, let's apply this pattern and find the 10th term. Starting from -8, if we keep multiplying by -0.5 for 10 times, we get:
-8 * (-0.5) * (-0.5) * (-0.5) * (-0.5) * (-0.5) * (-0.5) * (-0.5) * (-0.5) * (-0.5) = -8 * (-0.5)^10
Now, let me take a moment to do some math magic here... *poof*
Drumroll, please! The 10th term of this tricky progression is:
-8 * (-0.5)^10 = 0.0625
Ta-da! So, the 10th term is 0.0625. Who knew math could be so playful?
To find the 10th term of the given progression, we first need to identify the pattern. In this case, it is an alternating pattern between positive and negative numbers.
The first term is -8, the second term is 4, and the third term is -2.
To find the next term, we alternate between multiplying the previous term by -1 and dividing it by 2:
-8 * -1 = 8
4 / 2 = 2
-2 * -1 = 2
So, from this pattern, we can deduce that the terms will repeat as 8, 2, 2, 8, 2, 2, ...
Since the pattern repeats every three terms, we can divide 10 by 3 and find that there will be 3 complete repetitions and a partial repetition of the pattern.
3 complete repetitions * 3 terms = 9 terms
The 10th term will then be the next term in the pattern, which is 8.
Therefore, the 10th term of the given progression -8, 4, -2 is 8.
To find the 10th term of a progression, we need to first determine the pattern or rule that governs the sequence. In this case, we can observe that the pattern alternates between multiplying the previous term by -0.5 and then dividing the result by -2.
To illustrate this pattern, let's identify the individual terms of the sequence:
Term 1: -8
Term 2: -8 * (-0.5) = 4
Term 3: 4 / (-2) = -2
Term 4: -2 * (-0.5) = 1
Term 5: 1 / (-2) = -0.5
Term 6: -0.5 * (-0.5) = 0.25
Term 7: 0.25 / (-2) = -0.125
Term 8: -0.125 * (-0.5) = 0.0625
Term 9: 0.0625 / (-2) = -0.03125
Term 10: -0.03125 * (-0.5) = 0.015625
Therefore, the 10th term of the given progression is 0.015625.
a = -8
r = -1/2
A10 = ar^9 = -8(-1/2)^9 = -8/-512 = 1/64