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Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?
9. Sequences, Series, & Induction
Geometric Sequences
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find the term of the geometric sequence in which and .
A
5120
B
1280
C
10240
D
2560
Verified step by step guidance1
Identify the formula for the nth term of a geometric sequence, which is given by: \( a_n = a_1 \cdot r^{(n-1)} \).
Substitute the given values into the formula: \( a_1 = 5 \), \( r = 2 \), and \( n = 10 \).
Calculate the exponent part of the formula: \( r^{(n-1)} = 2^{(10-1)} = 2^9 \).
Multiply the first term by the result of the exponentiation: \( a_{10} = 5 \cdot 2^9 \).
Simplify the expression to find the 10th term of the sequence.
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