Question

Find the 27th term of the arithmetic sequence 15, 17.25, 19.5, 21.75,...

Answer 1

Answer:

Step-by-step explanation:

Find the Pattern -

The Pattern in the sequncesequence above would +2.25, so I assume the answer would be 73.5.

Answer 2

Answer:

The 27th term is 73.5.

Step-by-step explanation:

We want to find the 27th term of the arithmetic sequence:

15, 17.25, 19.5, 21.75, ...

We can write a direct formula. Recall that the direct formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term and d is the common difference.

From the sequence, we can see that our initial term a is 15.

To find the common difference, subtract a term and its previous term. Thus, the common difference will be:

$d=17.25 - 15 = 2.25$

Thus, our direct formula is:

$x_n=15+2.25(n-1)$

To find the 27th term, let n = 27. Substitute and evaluate:

$\displaystyle \begin{aligned} x_{27} &=15+2.25((27)-1) \\ &= 15+2.25(26) \\&= 15+58.5 \\ &= 73.5\end{aligned}$

Thus, the 27th term is 73.5.