Question

Consider the first three terms of the arithmetic sequence 9,14,19Determine d , the common difference Find the nth term, TnDetermine T9, the 9th term in the sequence

Answer 1

Answer:

The common difference, d = 5

`\begin{gathered} T_n=5n+4 \\ T_9=49 \end{gathered}`Step-by-step explanation:

The given sequence is:

9, 14, 19

The common difference is the difference between the consecutive terms of the sequence.

The common difference, d = 14 - 9 or d = 19 - 14

Therefore, the common difference, d = 5

The nth term of an Arithmetic sequence is given by the formula:

`T_n=a+(n-1)d`

where the first term, a = 9

The common difference, d = 5

Substitute a = 9, and d = 5 into the nth term formula above

`\begin{gathered} T_n=9+5(n-1) \\ T_n=9+5n-5 \\ T_n=5n+4 \end{gathered}`

The 9th term in the sequence is calculated by substituting n = 9 into the nth term gotten above

`\begin{gathered} T_n=5n+4 \\ T_9=5(9)+4 \\ T_9=45+4 \\ T_9=49 \end{gathered}`