Question

Identify the 25th term of an arithmetic sequence where a1 = −7 and a18 = 95

Answer 1

The 25th term is 137

Step-by-step explanation:
`\begin{gathered} \text{Given:} \\ a_1\text{ = -7} \\ a_(18)\text{ = 95} \\ a_(25)\text{ = ?} \end{gathered}`

To get the 25th term, we need to find the common difference.

An arithmetic sequence is given as:

`\begin{gathered} a_n=a_1\text{ + (n - 1)d} \\ \text{where a}_1\text{ = first term} \\ n\text{ = number of terms} \\ d\text{ = co}mmon\text{ difference} \end{gathered}`

The formula for the 18th term will be used to find the common difference:

`\begin{gathered} \text{where n = 18} \\ a_(18)=a_1\text{ + (18 - 1)(d)} \\ 95\text{ = -7 + 17d} \\ 95\text{ + 7 = 17d} \\ 102\text{ = 17d} \\ d\text{ = }(102)/(17) \\ d\text{ = 6} \end{gathered}`

Now we can find the 25th term:

`\begin{gathered} \text{where n = 25} \\ a_(25)=a_1\text{ + (25 - 1)d} \\ a_(25)=a_1\text{ + 24d} \\ a_(25)=\text{ -7 + 24(6) }=\text{ 144 - 7} \\ a_(25)=\text{ }137 \end{gathered}`

The 25th term is 137