SOLUTION: Please help me solve! Give the general term of the set. Type the general term using n. {7, 10,13, 16, 19, ......}

Question 124231: Please help me solve!
Give the general term of the set. Type the general term using n.
{7, 10,13, 16, 19, ......}

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There is some starting point and for each term you add three. That means there are n 3s in the nth term. Since 7 is the number 1 term, there must be 1 3 added to the starting point to get the value 7.

Now we have a picture of what is going on and we can re-write the first few terms of the set thus:

{4+1(3),4+2(3),4+3(3),...}

Notice that the first term has a multiplier of 1, the second has a multiplier of 2, and the third term a multiplier of 3. This pattern leads us to the conclusion that the nth term should have a multiplier of n.

So, the general term, in terms of n is

Adding 3 to 19 should give the 6th term as 22. , so our answer checks.
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