Question

Find the 77th term of the arithmetic sequence 8, 26, 44, ...​

Answer 1

Answer: 1,376

Step-by-step explanation: All we need to do is take our explicit formula and plug in the information we need to know for the problem.

Explicit formula - $a_{n} = a_{1} + (n - 1) d$

We are trying to find the 77th term of this sequence so we first have $a_{77}$.

We know $a_{1}$ is 8 because that's the first term in our arithmetic sequence.

The variable n represents the number of terms we're trying to solve for which is 77. So that will be 77 - 1 and then we are going to multiply that by our common difference which is 18.

So plugging into the formula, we have $a_{77} = 8 + (77 - 1)18$

So now we can go ahead and simplify this

information and see what we get.

So simplifying inside parentheses first, we get 76 and we multiply that by 18 to get 1,368.

So therefore we have $a_{77} = 8 + 1,368$ which is 1,376.