Write an expression to describe the sequence below, and then find the 8th term. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
The sequence is: 5, 8, 11, 14, 17, ...
To describe the sequence, we can use the expression 3n + 2.
To find the 8th term, we can substitute n = 8 into the expression: 3(8) + 2 = 24 + 2 = 26.
Therefore, the 8th term of the sequence is 26.
To describe the sequence, we notice that each term is obtained by adding 3 to the previous term. Therefore, the expression to represent the sequence is:
term(n) = term(n-1) + 3
To find the 8th term, we can substitute n = 8 into the expression:
term(8) = term(8-1) + 3
term(8) = term(7) + 3
Now, we need to find term(7), which can be obtained by substituting n = 7 into the expression:
term(7) = term(7-1) + 3
term(7) = term(6) + 3
Continuing this process, we find:
term(6) = term(6-1) + 3
term(6) = term(5) + 3
term(5) = term(5-1) + 3
term(5) = term(4) + 3
term(4) = term(4-1) + 3
term(4) = term(3) + 3
term(3) = term(3-1) + 3
term(3) = term(2) + 3
term(2) = term(2-1) + 3
term(2) = term(1) + 3
Now, we can substitute the values back into the expression to find term(8):
term(8) = (term(7) + 3) + 3
term(8) = ((term(6) + 3) + 3) + 3
term(8) = (((term(5) + 3) + 3) + 3) + 3
term(8) = ((((term(4) + 3) + 3) + 3) + 3) + 3
term(8) = (((((term(3) + 3) + 3) + 3) + 3) + 3) + 3
term(8) = ((((((term(2) + 3) + 3) + 3) + 3) + 3) + 3) + 3
term(8) = (((((((term(1) + 3) + 3) + 3) + 3) + 3) + 3) + 3) + 3
Since the first term (term(1)) is not given, we cannot compute the exact value of term(8) without knowing the first term.