Use inductive reasoning to predict the next number in the sequence.
4) 1, -1/4, 1/16, -1/64, 1/256, . .
1/4^n then change from positive to negative alternatively.
then sequence shown goes to n=5.. therefore the next value at n=6 should be -1/4^6 = -1/1024
To use inductive reasoning to predict the next number in the sequence, we need to look for a pattern or relationship between the given numbers.
Observing the given numbers: 1, -1/4, 1/16, -1/64, 1/256, ...
We can see that each number in the sequence alternates between positive and negative. Additionally, each number is a fraction with a power of 4 as the denominator, starting from 4^0 (which is 1) and increasing by 4 for each subsequent term.
Based on this pattern, we can predict that the next number in the sequence will be -1/1024.
To predict the next number in this sequence using inductive reasoning, we need to identify the pattern or rule governing the sequence.
Looking at the sequence: 1, -1/4, 1/16, -1/64, 1/256, ...
Let's examine the denominators of each term: 1, 4, 16, 64, 256.
The pattern becomes clear: the denominator is a power of 4, starting from 4^0 and increasing by 1 exponent with each subsequent term.
So, the next term in the sequence should have a denominator of 4^5 (since we are starting with 4^0).
Calculating 4^5 gives us 1024 as the denominator. Since the sign alternates between positive and negative, the numerator will be -1.
Therefore, the next number in the sequence should be -1/1024.