Given the sequence 17, 21, 25,...589

a) Find the 123rd term in this sequence.

looks like an arithmetic sequence where

a = 17, d = 4

term(123) = a +122d
= 17 + 122(4) = 505

btw, 589 = 17 + 4(n-1)
589 = 17 + 4n - 4
4n = 576
n = 144
there are 144 terms in the sequence

To find the 123rd term in the given sequence, we need to find the pattern or rule that relates the terms. Let's analyze the sequence to find a common difference.

Looking at the given sequence: 17, 21, 25,..., we can observe that each term is obtained by adding 4 to the previous term.

So, the rule or pattern can be defined as "Each term is obtained by adding 4 to the previous term."

Now, we can use this pattern to find the 123rd term. Starting with the first term, 17, we can add (123 - 1) * 4 to it to reach the 123rd term.

123 - 1 = 122
122 * 4 = 488

Finally, we add 488 to the first term, 17:

17 + 488 = 505

Therefore, the 123rd term in the sequence is 505.