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# Formula of the general term of a PA

We already know that in a PAN: Note that we can write all the terms of a PAN in function of and r: Therefore, the general term of PAN will be given by the formula: , no  • = first term
• = nth term
• r = reason
• no = number of terms

Example 1

Determine the general term of PA (-19, -15, -11,…):

Resolution  The general term of PA (-19, -15, -11,…) é .

Example 2

Determine the 16th term of the PA (3, 9, 15,…):

Resolution  Therefore, the 16th term of PA (3, 9, 15,…) é 93.

Example 3

Interpolate six arithmetic means between -8 and 13:

Resolution

From the statement we have to:  Once reason is found, just interpolate the arithmetic means: (-8, -5, -2, 1, 4, 7, 10, 13).

Example 4

How many multiples of 5 there is between 101 and 999?

Resolution

• The first multiple of 5 after 101 é 105, therefore = 105;
• The last multiple of 5 before 999 é 995, therefore = 995;
• The reason is 5because we are referring to multiples of 5. Thus, we conclude that there are 179 multiples of 5 in between 101 and 999.

Example 5

Knowing that in a PAN the 2nd term is 9 and the 11th term is 45, write this PAN:

Resolution
Let's write these terms as a function of and r: We set up a system of equations: Therefore, the PAN é (5, 9, 13, 17,… ).

Next: Sum of the N Terms of a PA