Given the explicit formula: a5= 8 + 7(n − 1)
What is the common difference?
What is the initial term?
What term is the formula finding?
What value should replace n?
The common difference can be determined by finding the difference between any two consecutive terms. In this case, the difference between a5 and a4 is 7. Therefore, the common difference is 7.
The initial term (a1) is found by substituting 1 for n in the formula. Thus, a1=8 + 7(1-1) = 8 + 7(0) = 8 + 0 = 8. Therefore, the initial term is 8.
The formula is finding the nth term of the sequence. In this case, the formula is finding the 5th term (a5).
To find the value that should replace n, it depends on which term of the sequence you are interested in finding. In this case, since the formula is finding the 5th term, the value that should replace n is 5.