What are the values of a1 and r in the geometric series 2, 2, 2, 2, 2?

In a geometric series, we denote the first term as a₁ and the common ratio as r. Let’s analyze the series given: 2, 2, 2, 2, 2.

First term (a₁):
The first term of this geometric series is simply the first number listed in the series, which is 2. Therefore, a₁ = 2.

Common ratio (r):
To find the common ratio, we divide any term by its preceding term. In this case, the terms are:
– The second term (2) divided by the first term (2): r = 2 / 2 = 1
– The third term (2) divided by the second term (2): r = 2 / 2 = 1
– This applies to all terms in the series.

Since the ratio is the same between all consecutive terms, we conclude that r = 1.

Summary:
In the geometric series 2, 2, 2, 2, 2:
– The value of a₁ is 2.
– The value of r is 1.