Question

Find the 24th term of the arithmetic sequence: 3/2, 3, 9/2, 6, .....

Answer 1

To determine an arithmetic sequence, to each number you add a constant to determine the next one in the sequence.

This constant is called "common difference" is symbolized as "d" and you can calculate it by subtracting the previous value of the sequence:

`d=3-(3)/(2)=(3)/(2)`

If "a" represents the first value of the sequence, we can say that the following values are determined as:

{a, a+d, a+2d, a+3d........a+nd}

Where "n" represents any value further away in the sequence, except the first one.

With this we can establish a rule to calculate the values of the sequence:

`x_n=a+d(n-1)`

xₙ represents the value in the nth position

d is multiplied with "n-1" because for the first value of the sequence, the common difference is not added.

So to calculate the 24th term of the sequence with a=3/2 and d=3/2 use the formula above and replace it with n=24

`\begin{gathered} x_(24)=a+(3)/(2)(24-1) \\ x_(24)=(3)/(2)+(3)/(2)23 \\ x_(24)=(211)/(6) \end{gathered}`

The 24th value of the sequence is 211/6