What is the 22nd term of the arithmetic sequence 12, 17, 22, 27, ...?

Answer:the 22nd term is 117

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1) d

Where

a represents the first term of the sequence.

d represents the common difference between successive terms.

n represents the number of terms in the sequence.

From the information given,

a = 12

d = 17 - 12 = 22 - 17 = 27 - 22 = 5

n = 22

We want to determine the value of the 22nd, T22. Therefore,

T22 = 12 + (22 - 1) 5

T22 = 12 + 105 = 117

In simple words you just find what is being added to each term in order to get the next term. Subtracting 17 by 12 you get 5, 22 minus 17 is 5 as well. Now that what is being added is found, you go by the last term given which is 27. You keep adding 5 to the number until you get to the 22nd term which would result in 117. If you would want to know the equation in order for it to be plugged in then you would use f (x) = 7+5x. You would want to use this equation instead of f (x) = 12+5x because putting 1 as x would make it equal to 17 which is NOT the first term but the second.