Question

Find the 94th term of the arithmetic sequence minus, 26, comma, minus, 37, comma, minus, 48, comma, dot dot dot−26,−37,−48,...

Answer 1

To find the 94th term of the arithmetic sequence given by \(-26, -37, -48, \ldots\), we first need to identify the first term and the common difference of the sequence.

The first term \(a\) is:
\[
a = -26
\]

Next, we calculate the common difference \(d\). The common difference can be determined by subtracting the first term from the second term:
\[
d = -37 - (-26) = -37 + 26 = -11
\]

Now, we can use the formula for the \(n\)-th term of an arithmetic sequence, which is given by:
\[
a_n = a + (n-1)d
\]

We want to find the 94th term (\(n = 94\)):
\[
a_{94} = -26 + (94 - 1)(-11)
\]

Calculating \(94 - 1\):
\[
94 - 1 = 93
\]

Now substitute this back into the formula:
\[
a_{94} = -26 + 93 \times (-11)
\]

Now we calculate \(93 \times (-11)\):
\[
93 \times (-11) = -1023
\]

Substituting this value back in:
\[
a_{94} = -26 - 1023
\]

Now perform the addition:
\[
a_{94} = -1049
\]

Thus, the 94th term of the arithmetic sequence is:
\[
\boxed{-1049}
\]