micv
A sequence Q consists of 15 numbers arranged in ascending order. The first term in this sequence is 25. In this sequence, for the first 14 terms, the ratio of the term to the next term is a fixed constant. The last term of the sequence is four times the first term. What is the 8th term in the sequence?
A) 50
B) 62.5
C) 25(4)^7
D) 25(2)^(8/7)
E) 25(2)^(8/15)
Given:
1. A sequence Q consists of 15 numbers arranged in ascending order.
2. The first term in this sequence is 25.
3. In this sequence, for the first 14 terms, the ratio of the term to the next term is a fixed constant.
4. The last term of the sequence is four times the first term.
Asked: What is the 8th term in the sequence?
1. A sequence Q consists of 15 numbers arranged in ascending order.
n = 15
\(a_1<a_2<a_3<.....<a_{15}\)
2. The first term in this sequence is 25.
\(a_1 = 25\)
3. In this sequence, for the first 14 terms, the ratio of the term to the next term is a fixed constant.
Let the ratio be r
\(a_2 = a_1*r\)
\(a_n = a_1*r^{n-1} \)
4. The last term of the sequence is four times the first term.
\(a_{15} = 4 * a_1 = r^{14} * a_1\)
\(r^7 = 2\); \(r^7 = -2\) is not feasible since \(a_1<a_2<a_3<.....<a_{15}\)
The 8th term in the sequence = \(a_ 1 * r^7 = 25 * 2 = 50 \)
IMO A