Question

Write an equation for the $n$ th term of the arithmetic sequence. Then find $a_{25}$ . $8,16,24,32,\ ...$

Answer 1

The equation for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d. For the given sequence 8, 16, 24, 32, ..., a_25 = 200.

Step-by-step explanation:

The given sequence is 8, 16, 24, 32, ... and we need to find the equation for the nth term and calculate a25.

Since the common difference between consecutive terms is 8, the equation for the nth term in an arithmetic sequence is given by:

an = a1 + (n-1)d

Here, a1 is the first term (8) and d is the common difference (8).

Plugging in the values, we get:

an = 8 + (n-1)(8)

Now, to find a25, we substitute n = 25 into the equation:

a25 = 8 + (25-1)(8) = 8 + 24(8) = 8 + 192 = 200.