The expression 3 x n can be written 3n. Use n= 1,2,3 ..., 10 to evaluate the expression. Describe the set of ten numbers. Suppose the sequence continues ror values of n greater than 10. Do the numbers 12, 21, 30 or 210 appeae in the sequence?
when we type the letter xwe mean the letter
when we type * we mean "times".
so I think
3*n = 3n
3*1 = 3
3*2 = 6
3*3 = 9
3*4 = 12
.
.
3*10 = 30
well
what is 12/3 ?
4 right
so
3*4 = 12 is there all right
same for 21 and 30
what about 210
well 210/3 = 70
so
3*70 = 210 and it is in the sequence for n = 70
To evaluate the expression 3n for n = 1,2,3,...,10, we simply substitute the values of n into the expression and calculate the result.
For n = 1: 3 x 1 = 3
For n = 2: 3 x 2 = 6
For n = 3: 3 x 3 = 9
For n = 4: 3 x 4 = 12
For n = 5: 3 x 5 = 15
For n = 6: 3 x 6 = 18
For n = 7: 3 x 7 = 21
For n = 8: 3 x 8 = 24
For n = 9: 3 x 9 = 27
For n = 10: 3 x 10 = 30
The set of ten numbers obtained from evaluating the expression are: {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}.
Looking at the sequence continuing from n > 10, we can observe the following:
- Number 12 does appear in the sequence, as it occurs when n = 4.
- Number 21 also appears in the sequence, as it occurs when n = 7.
- Number 30 appears in the sequence, as it occurs when n = 10.
However, number 210 does not appear in the sequence, as it is not a multiple of 3.
To evaluate the expression 3n for n = 1, 2, 3, ..., 10, we simply substitute each value of n into the expression and calculate the result.
Let's calculate the expression for n = 1, 2, 3, ..., 10:
For n = 1: 3 x 1 = 3
For n = 2: 3 x 2 = 6
For n = 3: 3 x 3 = 9
For n = 4: 3 x 4 = 12
For n = 5: 3 x 5 = 15
For n = 6: 3 x 6 = 18
For n = 7: 3 x 7 = 21
For n = 8: 3 x 8 = 24
For n = 9: 3 x 9 = 27
For n = 10: 3 x 10 = 30
Based on these calculations, the set of ten numbers in the sequence is {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}.
Now, let's consider values of n greater than 10.
To check if the numbers 12, 21, 30, or 210 appear in the sequence, we need to determine if there exist values of n greater than 10 such that 3n equals any of these numbers.
For 3n to equal 12, n would have to be 4.
For 3n to equal 21, there is no whole number value of n that satisfies this equation.
For 3n to equal 30, n would have to be 10.
For 3n to equal 210, n would have to be 70.
Therefore, out of these four numbers, only 12 and 30 appear in the sequence, while 21 and 210 do not.