7 Consider the arithmetic sequence whose f first few entries

7. Consider the arithmetic sequence whose f first few entries are 3, 7, 11, 15, 19, 23, a. Determine the 50th entry in the sequen explain why your answer is correct, ahd b. Find an expression for the Nth entry in this sequence, and explain in detail wh pression is valid c. Is 207 an entry in the sequence? If yes, which entry? If no, why not? Determine the answer to these questions in two ways: with algebra in a way that a student in elementary school might be able to. and d. Is 100 an entry in the sequence? If yes, which entry? If no, why not? Determine the answer to these questions in two ways: with algebra and in a way that a student in elementary school might be able to.

Solution

3 , 7 , 11 , 15 , ....

Common difference = 7-3 = 4
First term, a1 = 3

an = a1 + (n-1)d

an = 3 + (n-1)*4

an = 4n - 1

a)
50th :
4(50) - 1
200 - 1
199

-------------------------------------------------------------------

b)
Nth :
a(N) = 4N - 1 ----> ANS

--------------------------------------------------------------------

c)
Checking if 207 works :
207 = 4N - 1
4N = 207 + 1
4N = 208
N = 208/4
N = 52
So, we got an integer value for N

Thus, 207 is part of the sequence

-------------------------------------------------------------------

d)
100 = 4N - 1
4N = 101
N = not integer

So, 100 is not part of the sequence