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22. Find the 20th term: -30, -22, -14, -6, ....(Hint: Finding the nth term if an Arithmetic Sequence formula: a, = a, + (n − 1)d. )

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Arithmetic Sequences

It consists in a series of terms with the condition that each term is calculated as the previous term plus a fixed number called the common difference (d).

The sequence is given as:

-30, -22, -14, -6,...

First, we need to find the common difference by subtracting two consecutive terms:

d = -22 - (-30) = -22 + 30 = 8

We can try another couple of terms:

d = -14 - (-22) = -14 + 22 = 8

If we test all the consecutive terms, we'll find the same value of d.

Now to use the formula:

an = a1 + (n - 1) * d

We need to find a1, the first term of the sequence. The value of a1 is -30.

Now we are ready to find the 20th term of the sequence (n=20) by substituting the values in the formula:

a20 = -30 + (20 - 1) * 8

Calculating:

a20 = -30 + 19 * 8 = -30 + 152 = 122

Thus the 20th term is 122

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