Answer:
Seventh term is 64
Sum of the first seven terms is 127
Step-by-step explanation:
The common ratio is 2
n = 7 and the first term is 1. So,
Seventh term is 64
Sum of the first seven terms is 127
Answer:
C
Step-by-step explanation:
Since they're the same factor being raised to a power. Treat them as a log of 2.
Log² 48 - 38
Log² 2
= 2²
Answer:
<h2>
Tₙ = -3(2)ⁿ</h2>
Step-by-step explanation:
The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;
a is the first term of the geometric sequence
r is the common ratio
n is the number of terms
If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;
T₁₂ = ar¹²⁻¹
T₁₂ = ar¹¹
Given T₁₂ = -12,288 and r = 2, we can calculate the first term a
-12,288 = a2¹¹
a = -12,288/2¹¹
a = -12,288/2048
a = -6
Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;
Tₙ = -6(2)ⁿ⁻¹
Tₙ = -6 * 2ⁿ * 2⁻¹
Tₙ = -6 * 2ⁿ * 1/2
Tₙ = -3(2)ⁿ
Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ
