A few days ago
Angel T

# Geometric Sequence?

1) If the first term in a geometric sequence is 7, and the third term is 63, what is the ninth term?

A) 367

B) 567

C) 2209

D) 45927

E) 165274

2) The first term in a certain geometric sequence is x and the fourth term in the sequence is 27x, where x is a nonzero number. Which of the following represents the tenth term?

A) 26x

B) 27

C) 154x

D) 4327x

E) 19683x

A few days ago

Question 1.

Well, without the second term, this sequence is a challenge, however, in my best guess, i would have to say the equation for the geometric sequence in question 1 is:

x = 7 * 3^(n-1)

where x is a value in the sequence, and n is the number of term of the sequence where the 1st term = 1, the 2nd term =2, and so on.

so for the 9th term

x = 7 * 3^(n-1)

x = 7 * 3^(9-1)

x = 7 * 3^(8)

x = 7 * 6561

x = 45927

Therefore, the answer is D) 45927

Question 2.

Similarily, without other terms, the equation for the sequence is tricky but I believe it is:

y = x * 3^(n-1)

where y is a value in the geometric sequence, x is a nonzero number, and n is the number term in the sequence, just like in Question 1.

so for the 10th term

y = x * 3^(10-1)

y = x * 3^(9)

y = x * 19683

y = 19683x

therefore the answer is E) 19683x

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