Question

mn+10+7(n-1) 18th term

Answer 1

To find the 18th term of the given expression \( mn + 10 + 7(n-1) \), we need to first simplify the expression.

1. Start with the expression:
\[
mn + 10 + 7(n - 1)
\]

2. Simplify \( 7(n - 1) \):
\[
7(n - 1) = 7n - 7
\]

3. Substitute this back into the expression:
\[
mn + 10 + 7n - 7
\]

4. Combine the constant terms:
\[
= mn + 7n + (10 - 7)
\]
\[
= mn + 7n + 3
\]

Now, we rewrite the expression for the general term:
\[
T(n) = mn + 7n + 3
\]

To find the 18th term (i.e., \( T(18) \)):
\[
T(18) = m(18) + 7(18) + 3
\]

Calculate \( 7(18) \):
\[
7 \times 18 = 126
\]

Now substituting this back into the original expression for \( T(18) \):
\[
T(18) = 18m + 126 + 3
\]
\[
= 18m + 129
\]

Thus, the 18th term is:
\[
\boxed{18m + 129}
\]