(7) What is the missing number? $$ 725,825,925, \ldots, 1125 $$

Question

UpStudy AI · Accepted Answer

Let's denote the sequence as follows:

$$
\begin{aligned}
a_1 &= 725, \
a_2 &= 825, \
a_3 &= 925, \
a_4 &= ?, \
a_5 &= 1125.
\end{aligned}
$$

We observe that the difference between consecutive terms is:

$$
a_2 - a_1 = 825 - 725 = 100 \quad \text{and} \quad a_3 - a_2 = 925 - 825 = 100.
$$

Since the difference is consistent, the sequence is an arithmetic sequence with a common difference of $$ d = 100 $$.

The formula for the $$ n $$-th term of an arithmetic sequence is:

$$
a_n = a_1 + (n-1)d.
$$

For the fourth term ($$ n = 4 $$):

$$
a_4 = 725 + (4-1)100 = 725 + 300 = 1025.
$$

Thus, the missing number is:

$$
\boxed{1025}
$$
The missing number is 1025.

(7) What is the missing number? \( 725,825,925, \ldots, 1125 \)