Is the number 1 a term in the sequence above?
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Is the number 1 a term in the sequence above?
To determine if the number 1 is a term in the sequence given by , we set the expression equal to 1:
Now, solve for :
Divide both sides by 15 to solve for :
Simplify the fraction:
The result, , is not an integer. Since must be a positive integer in sequence indexing, there is no valid solution for integer . Therefore, the number 1 cannot be a term of this sequence.
The correct answer is No.
No.
Look at the following set of numbers and determine if there is any property, if so, what is it?
\( 94,96,98,100,102,104 \)
In sequences, n represents the position of a term (1st term, 2nd term, etc.). You can't have the 7/5th term - positions must be whole numbers!
If n comes out as a decimal or fraction, the number you're testing cannot be a term in the sequence. Only integer solutions for n produce valid sequence terms.
Set and solve for n. If n is a positive integer, then yes! If n is negative, zero, or fractional, then no.
Substitute positive integers: n=1 gives -5, n=2 gives 10, n=3 gives 25, etc. The sequence is -5, 10, 25, 40, 55...
You could, but that's inefficient! Setting up an equation like gives you the exact answer much faster than guessing.
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