what are hte numbers?

Question

what are the first 5 numbers:

1. "start at 10,double the number before this one,and subtract 1".

2. "start at 2, triple each number and add 1".

Answer 1

1. the number before 10 is 9
multiply by two
9 *2 = 18
subtract 1
18 - 1 = 17

then for 17
16*2 = 32
32 - 1 = 31

then for 31
30 * 2 = 60
60-1 = 58

then for 58
58 * 2 = 116
116-1=115

that is the first five numbers (including 10):
10, 17, 61, 58, 116

2. multiply two by three
2 * 3 = 6
add one
6 + 1 = 7

then for 7
7*3 = 21
21+1 = 22

then for 22
22*3 = 66
66+1=67

then for 67
67*3 = 201
201+1=202
the first 5 numbers are 2, 7, 22, 67, 202

Answer 2

Those are recursive formulas, in which the formula contains a reference to itself. The key part is the second phrase in the sentence:
"double the number before this one and subtract 1" If X_n is the number you are looking at, you get it by doubling the one before it (X_n-1) and subtracting 1. Therefore the recursive formula is

X_n = 2*(X_n-1) - 1

To get the sequence, start at X_0 which is the first number. That was given to you as being 10. So

X_1 = 2*(X_0) - 1 = 2*10 - 1 = 19

Now that you know x_1, you can get x_2 from the same formula:

X_2 = 2*(X_1) - 1 = 2*19 - 1 = 37 (EDITED)

you can get all the numbers you want this way.

The second problem is solved in exactly the same manner.

Answer 3

1. 2(n-1) -1= x, where n starts as 10 then n-1 will be equal to 9 and then becomes your answer, or x. 2(9)-1=17, then n is 17 the second time you use this equation....the first 5 numbers are 17, 31, 61, 121, 241. each answer is one less than one less twice the number before it, confirming our equation.

2. 3n+1=x, where n starts as 2. The answers are 7, 22, 67, 202, 607. each number is triple the number before it, plus one.......

sorry if my answers are wrong.......

but hope this is correct because it is very familiar to me.......it is like an IQ test...