Damian filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every ho
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We have been given the sequence 2,3,5,9,17.
We can write the terms of this sequence as
From the above term we can see that for the first term we take exponent 0 on 2 and then add 1 .
For second term we take exponent 1 on 2 and then add 1 .
For third term we take exponent 2 on 2 and then add 1 .
Using this fact for the next term of the sequence i.e. 6th term, we can take exponent 5 on 2 and then add 1 .
Therefore, next term of the sequence is given by
Therefore, the next term is 33.
Using the above facts, the pattern is given by
No, it is impossible. Intuitively, a negative number sits at the left of 0 on the number line, and a positive number sits at the right of 0 on the number line. And a number x is greater than another number y if x sits at the right of y on the number line. So, every positive number is greater than any negative number.
Also, by definition, a positive number is greater than 0, and a negative number is smaller than zero. So, if x is positive and y is negative, you have
and since the relation of order "<" is transitive, this implies