1003112810
Level:
B
The sum of the first \( n \) terms of a geometric sequence is \( -5 \), the common ratio is \( -2 \) and the first term equals \( 1 \). Find \( n \).
\( 4 \)
\( 3 \)
\( 5 \)
\( 6 \)
\( 2 \)
Geometric sequences
1003112809
Level:
A
The first term of a geometric sequence is \( 16 \) and the fourth term equals \( 54 \). Which of the following inequalities is true for the second term of the sequence?
\( a_2 > a_1 \)
\( a_2 < a_1 \)
\( a_2 < 0 \)
\( a_2 > a_4 \)
\( a_2 < \frac{a_4}{a_1} \)
1003112808
Level:
B
The first term of a geometric sequence is \( 15 \) and the common ratio is \( -1 \). Find the sum of the first \( 10 \) terms of this sequence.
\( 0 \)
\( 15 \)
\( -15 \)
\( 150 \)
\( -150 \)
1003112807
Level:
B
The sum of the first two terms of a geometric sequence is \( 28 \) and its first term equals \( 2 \). Which of the following statements about its common ratio \( q \) is not valid?
\( q \) is an even number.
\( q > 10 \)
\( q < 28 \)
\( q \) is prime number.
\( q \) is a divisor of \( 26 \).
1003112806
Level:
B
The sum of the first four terms of a geometric sequence is \( 0 \) and the first term equals \( 2 \). Choose the correct formula to find the eighth term.
\( a_8 = 2\cdot (-1)^7 \)
\( a_8 = 2\cdot (1)^7 \)
\( a_8 = 2\cdot 2 \)
\( a_8 = \frac02 \)
\( a_8 = 2\cdot (-2) \)
1003112805
Level:
A
The \(n\)th term of a geometric sequence is \(\frac52 \), the common ratio is \( \frac12 \) and the fourth term is \( 20 \). Find \( n \).
\( 7 \)
\( 8 \)
\( 6 \)
\( 10 \)
\( 5 \)
1003112804
Level:
B
The third term of a geometric sequence is \( -5 \) and the eighth term is \( -5 \). \( s_5 \) is the sum of the first five terms and \( q \) is the common ratio of this sequence. Choose the formula which is not valid for this sequence:
\( s_5=-5\cdot\frac{q^5-1}{q-1} \)
\( s_5=-25 \)
\( s_5=5\cdot a_1 \)
\( s_5=5\cdot a_3 \)
\( s_5=5\cdot(-5) \)
1003112803
Level:
A
The second term of a geometric sequence is \( 24 \) and the fifth term is \( 3 \). Choose the correct formula to find the third term of this sequence.
\( a_3=24\cdot\sqrt[3]{\frac3{24}} \)
\( a_3=24\cdot\sqrt[3]{\frac{24}3} \)
\( a_3=3\cdot\sqrt[3]{\frac3{24}} \)
\( a_3=3\cdot\sqrt[3]{\frac{24}3} \)
\( a_3=8\cdot\sqrt[3]{\frac3{24}} \)
1003112802
Level:
A
The first term of a geometric sequence is \( -36 \) and the fourth term is \( -\frac{32}3 \). Find the common ratio.
\( \frac23 \)
\( -\frac23 \)
\( \frac32 \)
\( -\frac32 \)
\( \frac13 \)
1003112801
Level:
A
The third term of a geometric sequence is \( 100 \) and the common ratio is \( -5 \). Find the first term of this sequence.
\( 4 \)
\( -4 \)
\( 20 \)
\( -20 \)
\( 500 \)