With the following problems and you

Just add the numbers in front of variables if the variables are the same! 
2) 5x+7+2x=7x+7 Because you would add the 5 and 2, and since the 7 doesn't have a variable you add it onto the end.
3) 16+4p (13p-9p is 4p)
4) y^2 +  5y (you can't combine y^2 with a y variable because it has a different exponent! if there is no exponent shown it is assumed to be 1. If exponents are the same you combine them, but if not you leave it as is)
5) You distribute the 5 (multiply) with 2h and 3, leaving 10h+15+3h which is 13h+15
6) 19+4n (12+7 is 19, and 18n-14n is 4n)
7) Distribute the 2 to get 18+10k
8) Distribute the 5 to get 15m+10
9) Distribute the 6 to get 6g+6h (you can't combine these because they are different variables)
10) The GCF of 4 and 8 is 4. Place the 4 out of the parentheses. Divide 4d and 8 by four and place them inside the parentheses. 4d is 4 times d so if you divide 4 by 4 you're left with 1d or just d. 8 divided by four is two. 4(d+2)
11) GCF= 7 so 7(3p+5q) 
12) GCF= 9 so 9(2x+y)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for