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QuestionHow many terms are in these sequences? a. 35,36,37,…,43535,36,37,\ldots,435 b. 1,3,32,…,3601,3,3^{2},\ldots,3^{60} c. 1000,2000,…,5000001000,2000,\ldots,500000 d. 1,3,9,…,65611,3,9,\ldots,6561

Studdy Solution

STEP 1

Question: Which of the following describes the sequence 35,36,37,38,…,43535,36,37,38, \ldots, 435?
A) Arithmetic sequence B) Geometric sequence C) Neither arithmetic nor geometric sequence D) Both arithmetic and geometric sequence
Answer: A) Arithmetic sequence

STEP 2

Question: What is the common difference (d) of the arithmetic sequence 35,36,37,38,…,43535,36,37,38, \ldots, 435?
A) 1 B) 2 C) 35 D) 435
Answer: A) 1

STEP 3

Question: Which of the following is the correct formula to find the nth term of the geometric sequence 1,3,32,33,…,3601,3,3^{2}, 3^{3}, \ldots, 3^{60}?
A) an=a1+(n−1)da_n = a_1 + (n - 1)d B) an=a1×r(n−1)a_n = a_1 \times r^{(n - 1)} C) an=a1+d(n−1)a_n = a_1 + d^{(n - 1)} D) an=a1×n(r−1)a_n = a_1 \times n^{(r - 1)}
Answer: B) an=a1×r(n−1)a_n = a_1 \times r^{(n - 1)}

STEP 4

Question: If the first term of an arithmetic sequence is 1000 and the last term is 500000, with a common difference of 1000, how many terms are there in the sequence?
A) 500 B) 501 C) 499 D) 1000
Answer: A) 500

STEP 5

Question: For the geometric sequence 1,3,9,27,81,243,…,65611,3,9,27,81,243, \ldots, 6561, if the common ratio is 3, how many terms are there in the sequence?
A) 8 B) 9 C) 10 D) 11
Answer: B) 9

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