If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be
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Answer:
Step-by-step explanation:
In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.
Now we can solve for the function by multiplying/subtracting/adding our known values.
Starting with the first term to the last term:
<u><em>WAIT</em></u><em>!</em><em> How is this possible? </em> (according to my calculator), and
, not 3!
It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use as an example.
What your calculator did was follow BEMDAS since it wasn't explicitly told not to.
BEMDAS:
- Brackets
- Exponents
- Multiplication/Division
- Addition/Subtraction
Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.
So rather than being <em>"-2 squared"</em> - it's <em>"the negative of of 2 squared."</em>
Tying this back into our problem, the squared method would only be true if it looks like . However, since we're substituting in -1, it looks like
, so the expression reads out as "<u><em>-1 to the fourth.</em></u>"
MULTIPLYING -1 by itself 4 times results in .
Applying this logic to our original term, :
Therefore, our first term is 3.
Let's move on to our second and third terms.
Second term:
Applying the same logic from our first term:
Third term:
-3 is just -3, no influence of x.
Combining our terms, we have .
This comes out to be -7, hence, the value of for our function
is <u>-7</u>.
Hope this helped!