Question

What is the 25th term of the arithmetic sequence where a1 = 8 and a9 = 48?

Answer 1

Answer:
`a_(25) = 128`

Explanation:

You need to use this formula:

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

Where
`a_n` is the nth] term,
`a_1` is the first term,"n" is the term position and "d" is the common diference.

You must find the value of "d". Substitute
`a_1=8`,
`a_9=48` and
`n=9` into the formula and solve for "d":

`48 = 8 + (9 - 1)d\\48=8+8d\\48-8=8d\\40=8d\\d=5`

Now, you can calculate the 25th term substituting into the formula these values:

`a_1=8`

`d=5` and
`n=25`

Then you get:

`a_(25) = 8 + (25 - 1)5`

`a_(25) = 8 + 120`

`a_(25) = 128`