Question

1. which geometric sequence has a first term equal to 55 and a common ratio of -5?

(55, 11, 2.2, 0.44, ...)
(55, 275, 1,375, 6,875, ...)
(55, -275, 1,375, -6,875, ...)
(-55, 11, -2.2, 0.44, ...)

Explanation:

⚡ Using what you learned: Geometric Sequences

Step 1: Identify the first term

The first term \( a_1 \) is given as:

$$ a_1 = 55 $$

Step 2: Calculate subsequent terms

Multiply each term by the common ratio \( r = -5 \) to find the next terms:

$$ a_2 = a_1 \cdot r = 55 \cdot (-5) = -275 $$

$$ a_3 = a_2 \cdot r = -275 \cdot (-5) = 1375 $$

$$ a_4 = a_3 \cdot r = 1375 \cdot (-5) = -6875 $$

Step 3: Match with the options

The sequence is:

$$ \{55; -275; 1,375; -6,875; \dots\} $$

This matches the third option.

Answer:

\( \{55; -275; 1,375; -6,875; \dots\} \) (the third option)