Question

Hello, I need help finding the value of the 89th term

Answer 1

Given:

common difference (d) = 7

6th term = 53

n = 6

Find: 89th term where n = 89

Solution:

To determine the 89th term, let's first determine the first term using the recursive formula for an arithmetic sequence.

`a_1=a_n-(n-1)(d)`

Let's use the given 6th term in which n = 6 and a₆ = 53. Use d = 7 for the common difference. Let's plug this into the recursive formula above.

`\begin{gathered} a_1=53-(6-1)(7) \\ a_1=53-(5)(7) \\ a_1=53-35 \\ a_1=18 \end{gathered}`

Therefore, the first term is 18.

Now, let's use the recursive formula again to determine the 89th term.

This time, we will use n = 89, d = 7, and a₁ = 18.

`a_n=a_1+(n-1)(d)`
`\begin{gathered} a_(89)=18+(89-1)(7) \\ a_(89)=18+(88)(7) \\ a_(89)=18+616 \\ a_(89)=634 \end{gathered}`

Therefore, the 89th term in the sequence is 634.