Question

1. which of these is an infinite arithmetic sequence?

(691, 632, 573, 514)
(232, 354, 476, 598, ...)
(845, 169, 33.8, 6.76, ...)
(724, 362, 181, 90.5)

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Identify infinite sequences

An infinite sequence continues indefinitely, indicated by an ellipsis ... at the end.

• \(\{691, 632, 573, 514\}\) is finite.
• \(\{232, 354, 476, 598, ...\}\) is infinite.
• \(\{845, 169, 33.8, 6.76, ...\}\) is infinite.
• \(\{724, 362, 181, 90.5\}\) is finite.

Step 2: Check for a constant difference

An arithmetic sequence has a constant difference \(d\) between consecutive terms:

$$ d = a_{n} - a_{n-1} $$

For \(\{232, 354, 476, 598, ...\}\):

$$ 354 - 232 = 122 $$

$$ 476 - 354 = 122 $$

$$ 598 - 476 = 122 $$

The difference is constant (\(d = 122\)).

For \(\{845, 169, 33.8, 6.76, ...\}\):

$$ 169 - 845 = -676 $$

$$ 33.8 - 169 = -135.2 $$

The difference is not constant (this is a geometric sequence with a common ratio of \(0.2\)).

Answer:

\(\{232, 354, 476, 598, ...\}\)