consider the arithmetic sequence:-4;-1;2;5...if the nth term of the sequence is 74 determine the value of n
I guess the first term is -4 and the difference is a = 3
Term n = term 1 + (n-1) a
Term n = -4 + (n-1) 3
for example
Term 3 = -4 + 2(3) = 2 , good, that works
so
Term n = -4 + (n-1)3 = 74
3(n-1) = 78
n-1 = 26
n = 27
To find the value of n for a given arithmetic sequence, where the nth term is known, we need to use the formula for the nth term of an arithmetic sequence.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Where:
an = nth term
a1 = first term
n = position of the term
d = common difference
In the given sequence, the first term (a1) is -4, and the common difference (d) is 3 (since each term increases by 3).
Now, we need to find the value of n for which the nth term (an) is 74.
Using the formula, we have:
74 = -4 + (n - 1) * 3
Simplifying the equation:
74 = -4 + 3n - 3
Adding 4 to both sides:
78 = 3n - 3
Adding 3 to both sides:
81 = 3n
Dividing both sides by 3:
n = 27
Therefore, the value of n is 27 for the given arithmetic sequence when the nth term is 74.