First of all, are you not gonna try any of those problems yourself at all? Anyway ...1). Doesn't it seems like it's increasing by 5?2). 1/(3^3) + 1/(3^4) + 1/(3^5) + 1/(3^6) and it's a geometric series and r = 1/3. You should be able to solve it by simply plug in the values in geometric series equation.3). Tn+2 = 3tn / 2tnT3 = T1+2 and so, n =1.T3 = 3(t1) / 2(t1) = 3(2) / 2(2) = 3/2.By the way, are you sure the problem is Tn+2 = 3tn / 2tn? it will gives you 3/2 for every term because tn cancels each other.4). I don't know what you mean5). I don't know what you mean6). T1 = 20  9(1) = 11T2 = 20  9(2) = 2T3 = 20  9(3) = 7So, your d = 9 in the arithematic sequence equation. To find the rest of the six terms, you can use arithematic sequence formula or just continue using Tn = 20  9n.7). Arithmetic sequence formula saysan=a1+(n1)d, so plug in last term is an=3, first term a1= 5, there are three terms in between, so that makes n = 53=5+(51)d 3=5+4d8=4dd=2start with 5 and then adding 2 to 5 gives 3, and adding 2 to 3 gives 1, and adding 2 to 1 gives 1. So, your answer is 3, 1 and 1.8). Look at my answer for 7 and you should try it yourself.9). Well, you start out with 20, so your a1 = 20, your d = 1 since each row has one additional seat. So, it's gonna be,20 + 21 + 22 + ... + 69The last row is going to be 20 + 49. So, an = 69. Now you have all the term and you should be able to figure out how to use the arithematic series formula.10). 5, 13, 21, .... and looks like it's adding 8. So, your a1 = 5, and your d = 8. You can continue from now.
