Question

For a given arithmetic sequence, the common difference, d, is equal to 3, and the 12th term, a12, is equal to 10.Find the value of the 73rd term, a73-a73 0=XŚ

Answer 1

ANSWER:

193

EXPLANATION:

Given:

Common difference, d = 3

12th term, a12 = 10

To find:

The value of the 73rd term

Let's go ahead and determine the first term using the arithmetic sequence formula as seen below;

$\begin{gathered} a_n=a_1+(n-1)d \\ \\ a_{12}=a_1+(12-1)3 \\ \\ 10=a_1+33 \\ \\ a_1=10-33 \\ \\ a_1=-23 \end{gathered}$

We can now go ahead and determine the 73rd term since we know that the first term is -23;

$\begin{gathered} a_n=a_1+(n-1)d \\ \\ a_{73}=-23+(73-1)3 \\ \\ a_{73}=-23+216 \\ \\ a_{73}=193 \end{gathered}$

Therefore, the value of the 73rd term is 193