1003057901
Level:
A
The \( 20 \)th term of an arithmetic sequence is \( 150 \) and the common difference is \( 3 \). Find the first term.
\( 93 \)
\( 90 \)
\( 87 \)
\( 210 \)
\( 207 \)
Arithmetic sequences
1003057902
Level:
A
The \( 13 \)th term of an arithmetic sequence is \( 64 \) and the \( 21 \)st term is \( 32 \). Find the common difference.
\( -4 \)
\( 4 \)
\( 8 \)
\( -8 \)
\( 2 \)
1003057903
Level:
A
The \( 17 \)th term of an arithmetic sequence is \( 77 \) and the common difference is \( 9 \). Choose the correct formula of calculation of the \( 5 \)th term.
\( a_5=77-12\cdot9 \)
\( a_5=17-12\cdot9 \)
\( a_5=12\cdot9-77 \)
\( a_5=77-16\cdot9 \)
\( a_5=77+12\cdot9 \)
1003057904
Level:
A
The \( 2 \)nd term of an arithmetic sequence is \( 3 \) and the \( 14 \)th term is \( 51 \). Choose the incorrect formula:
\( a_{20}=a_2+(51-3)\cdot18 \)
\( a_{20}=75 \)
\( a_{20}=a_{14}+6\cdot4 \)
\( a_{20}=a_2+18\cdot4 \)
\( a_{20}=3+\frac{18}{12} (a_{14}-a_2 ) \)
1003057905
Level:
A
The \( n \)th term of an arithmetic sequence is \( 76 \), the common difference is \( 6 \) and the first term is \( -2 \). Find the \( n \).
\( 14 \)
\( 12 \)
\( 13 \)
\( 15 \)
\( 11 \)
1003085101
Level:
A
The second term of an arithmetic sequence is \( 3 \) and the fourth term is \( -1 \). Find the recursive formula for the sequence.
\( a_1=5;\ a_{n+1}=a_n-2 \text{ for all } n\in\mathbb{N} \)
\( a_1=2;\ a_{n+1}=a_n-2 \text{ for all } n\in\mathbb{N} \)
\( a_1=3;\ a_{n+1}=a_n-1 \text{ for all } n\in\mathbb{N} \)
\( a_1=5;\ a_{n+1}=a_n-4 \text{ for all } n\in\mathbb{N} \)
\( a_1=3;\ a_{n+1}=a_n-4 \text{ for all } n\in\mathbb{N} \)
1003085102
Level:
A
The first term of an arithmetic sequence is \( 6 \) and the sixth term is \( 1 \). Find the recursive formula for the sequence.
\( a_1=6;\ a_{n+1}=a_n-1 \text{ for all } n\in\mathbb{N} \)
\( a_1=6;\ a_{n+1}=a_n+1 \text{ for all } n\in\mathbb{N} \)
\(a_1=1;\ a_{n+1}=a_n+5 \text{ for all } n\in\mathbb{N} \)
\( a_1=1;\ a_{n+1}=a_n-5 \text{ for all } n\in\mathbb{N} \)
1003085103
Level:
A
The third term of an arithmetic sequence is \( 3 \) and the common difference is \( 3 \). Find the \(n\)th term.
\( a_n=3n-6 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n-3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+3 \text{ for all } n\in\mathbb{N} \)
\( a_n=3n+6 \text{ for all } n\in\mathbb{N} \)
1003085104
Level:
A
The \( n \)th term of an arithmetic sequence is \( 1-3n \). Find the \( 5 \)th term and the common difference.
\( a_5=-14;\ d=-3 \)
\( a_5=-2;\ d=-3 \)
\( a_5=14;\ d=-3 \)
\( a_5=-14;\ d=3 \)
\( a_5=-2;\ d=3 \)
1003085208
Level:
A
Given an arithmetic sequence $(a_n)_{n=1}^{\infty}$, where $a_8=\frac83$, $a_k=8$ and the common difference is $\frac23$, find $k$.
$16$
$15$
$14$
$21$
$10$