Find the explicit term of the arithmetic sequence which first terms are the following.
-4, 2, 8, 14, 20, 26, 32, ...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 = -4
- d=6
Therefore:
a_n = -4+6\left(n-1\right)\\= -4+6n-6\\=6n-10
The explicit form of this sequence is a_n=6n-10.
-3, 1, 5, 9, 13, 17, 21, ...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 = -3
- d=4
Therefore:
a_n = -3+4\left(n-1\right)\\= -3+4n-4\\=4n-7
The explicit form of this sequence is a_n=4n-7.
3, 10, 17, 24, 31, 38,...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 = 3
- d=7
Therefore:
a_n = 3+7\left(n-1\right)\\= 3+7n-7\\=7n-4
The explicit form of this sequence is a_n=7n-4.
10, 7 ,4 ,1 ,-2 ,...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 = 10
- d=-3
Therefore:
a_n = 10-3\left(n-1\right)\\= 10-3n+3\\=-3n+13
The explicit form of this sequence is a_n=-3n+13.
101, 97, 93, 89, 85, 81,...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 =101
- d=-4
Therefore:
a_n = 101-4\left(n-1\right)\\= 101-4n+4\\=-4n+105
The explicit form of this sequence is a_n=-4n+105.
-17, -14, -11, -8, -5, -2,...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 = -17
- d=3
Therefore:
a_n = -17+3\left(n-1\right)\\= -17+3n-3\\=3n-20
The explicit form of this sequence is a_n=3n-20.
21, 14, 7, 0, -7, ...
We know that the following is the explicit formula of an arithmetic sequence whose first term is a_1 and common difference is d :
a_n= a_1+d\left(n-1\right)
Here, we have:
- a_1 =21
- d=-7
Therefore:
a_n = 21-7\left(n-1\right)\\= 21-7n+7\\=-7n+28
The explicit form of this sequence is a_n=-7n+28.