Question

If the ${{x}^{th}}$ position in a pattern of numbers is given by the expression 20 – 3x, then find the ${{15}^{th}}$ and ${{20}^{th}}$ terms.

Answer 1

Hint: We have given the relation between the position of a number in functionpattern and its numerical value by an expression 20 – 3x. so, to evaluate the number at ${{15}^{th}}$ and ${{20}^{th}}$, we will simply put the value of ${{15}^{th}}$ and ${{20}^{th}}$ in an expression 20 – 3x to get the numbers.

Complete step by step answer:
It is given that there are function patterns and the number of any ${{x}^{th}}$pattern in function is given by an expression 20 – 3x. so, which means if you want to find the number which is at ${{x}^{th}}$position in a collection of function patterns, then you will get the value of the number by using expression 20 – 3x.
In the same way, we will find the number in function patterns which are at ${{15}^{th}}$ and ${{20}^{th}}$ positions.
For ${{15}^{th}}$ position, we will just put the value of x equals to 15 in an expression 20 – 3x to find the number at ${{15}^{th}}$ position in function patterns.
Putting value of x equals to 15 in an expression 20 – 3x, we get
20 – 3(15) = 20 – 45
Subtracting 45 from 20, we get
20 – 45 = -25 .
Similarly, For ${{20}^{th}}$ position, we will just put the value of x equals to 15 in an expression 20 – 3x to find the number at ${{20}^{th}}$ position in function patterns.
Putting value of x equals to 20 in an expression 20 – 3x, we get
20 – 3(20) = 20 – 60
Subtracting 60 from 20, we get
20 – 60 = -40 .

So, The number which is at ${{15}^{th}}$ position in function patterns is equals to -25 and number which is at ${{20}^{th}}$ position in function patterns is equals to -40.

Note: You just have to understand what the question is demanding. Whenever you subtract a large number from the smaller number the sign turns from positive to negative. Calculation should be done carefully and accurately as it may affect the value number.