Write an expression for the most apparent nth term of the sequence. Assume n begins with 1.
3,7,11,15,19
My answer was an= 3 +4n but this wrong.
term(n) = a + (n-1)d
= 3 + 4(n-1)
= 3 + 4n - 4
= 4n - 1
check:
term(3) = 12-1 = 11, checks!
Thank You
To find the correct expression for the nth term of the sequence 3, 7, 11, 15, 19, we need to observe the pattern. In this sequence, each term is obtained by adding 4 to the previous term. However, the initial term is 3, not 0.
Therefore, the correct expression for the nth term would be:
an = 3 + 4(n - 1)
Let's check the values using this expression:
For n = 1: an = 3 + 4(1 - 1) = 3 + 4(0) = 3 (which is the first term in the original sequence)
For n = 2: an = 3 + 4(2 - 1) = 3 + 4(1) = 7 (which is the second term in the original sequence)
For n = 3: an = 3 + 4(3 - 1) = 3 + 4(2) = 11 (which is the third term in the original sequence)
For n = 4: an = 3 + 4(4 - 1) = 3 + 4(3) = 15 (which is the fourth term in the original sequence)
For n = 5: an = 3 + 4(5 - 1) = 3 + 4(4) = 19 (which is the fifth term in the original sequence)
Thus, the expression an = 3 + 4(n - 1) generates the correct terms for the given sequence.
To find the correct expression for the nth term of the sequence 3, 7, 11, 15, 19, let's first observe the pattern:
To get from 3 to 7, we add 4.
To get from 7 to 11, we add 4.
To get from 11 to 15, we add 4.
To get from 15 to 19, we add 4.
From this pattern, we can see that for each term, we are adding 4 to the previous term. However, the initial term is not 3, but rather 1. So we need to account for this difference.
To do that, we can subtract 2 from each term to align it with the sequence starting at 1:
1, 5, 9, 13, 17
Now, we can see that for each term, we add 4 to the previous term. This means that the nth term can be represented by the expression an = 1 + 4n.