Answer :
We are given a position-to-term rule for a sequence: "multiply by 4, then add 6." This means that the nth term in the sequence is found by multiplying the position number [tex]n[/tex] by 4 and then adding 6 to the result.
Let's denote the nth term of the sequence as [tex]a_n[/tex]. According to the given rule, we can write the formula for the nth term as:
[tex]a_n = 4n + 6[/tex]
Now, let's generate the first 10 terms of the sequence using this formula:
For the 1st term ([tex]n = 1[/tex]):
[tex]a_1 = 4 \times 1 + 6 = 4 + 6 = 10[/tex]For the 2nd term ([tex]n = 2[/tex]):
[tex]a_2 = 4 \times 2 + 6 = 8 + 6 = 14[/tex]For the 3rd term ([tex]n = 3[/tex]):
[tex]a_3 = 4 \times 3 + 6 = 12 + 6 = 18[/tex]For the 4th term ([tex]n = 4[/tex]):
[tex]a_4 = 4 \times 4 + 6 = 16 + 6 = 22[/tex]For the 5th term ([tex]n = 5[/tex]):
[tex]a_5 = 4 \times 5 + 6 = 20 + 6 = 26[/tex]For the 6th term ([tex]n = 6[/tex]):
[tex]a_6 = 4 \times 6 + 6 = 24 + 6 = 30[/tex]For the 7th term ([tex]n = 7[/tex]):
[tex]a_7 = 4 \times 7 + 6 = 28 + 6 = 34[/tex]For the 8th term ([tex]n = 8[/tex]):
[tex]a_8 = 4 \times 8 + 6 = 32 + 6 = 38[/tex]For the 9th term ([tex]n = 9[/tex]):
[tex]a_9 = 4 \times 9 + 6 = 36 + 6 = 42[/tex]For the 10th term ([tex]n = 10[/tex]):
[tex]a_{10} = 4 \times 10 + 6 = 40 + 6 = 46[/tex]
Therefore, the first 10 terms of the sequence generated by the rule "multiply by 4, then add 6" are:
[tex]10, 14, 18, 22, 26, 30, 34, 38, 42, 46[/tex]
This is the sequence you are looking for.
