Question

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

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

Explanation:

Step1: Recall geometric sequence formula

The \(n\)-th term of a geometric sequence is \(a_n = a_1 \times r^{n-1}\), where \(a_1=55\), \(r=-5\)

Step2: Calculate 2nd term

Substitute \(n=2\): \(a_2 = 55 \times (-5)^{2-1} = 55 \times (-5) = -275\)

Step3: Calculate 3rd term

Substitute \(n=3\): \(a_3 = 55 \times (-5)^{3-1} = 55 \times 25 = 1375\)

Step4: Calculate 4th term

Substitute \(n=4\): \(a_4 = 55 \times (-5)^{4-1} = 55 \times (-125) = -6875\)

Answer:

{55; -275; 1,375; -6,875; ...}