Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
The following steps provide a good method to use when solving linear equations. Simplify each side of the equation by removing parentheses and combining like terms. Use addition or subtraction to isolate the variable term on one side of the equation. Use multiplication or division to solve for the variable.
Answer: The general term of the sequence {1,4,9,16,25} is n^2.
The given sequence is: 1 , 4 , 9 , 16 , . . . . If you analyze the above sequence, you would see that it is a sequence of the squares of positive integers. Observing these terms, a n = n 2 .
Answer: nth term is n².
The general term of a number sequence is one of many ways of defining sequences. This sequence can be specified by using an explicit formula Tn=n+4 T n = n + 4 is the general term or th term formula for n=1,2,3,4,⋯ n = 1 , 2 , 3 , 4 , ⋯ .
Therefore, the \[{{n}^{th}}\] term of the sequence 1, 4, 9, 16, 25 is \[{{n}^{2}}\]. Note: Students should know that the given sequence in this problem has no common difference, so we cannot use any formulas to find the \[{{n}^{th}}\] term.
∴ for n=8, it will be, 82⇒64. Was this answer helpful?
Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
2n. 2n - 1. Therefore, 2n represents the general term for the sequence 2, 4, 6, 8, 10, . . ..
What are the four basic rules of algebra? The basic rules of algebra are the commutative rule of addition, the commutative rule of multiplication, the associative rule of addition, the associative rule of multiplication, and the distributive property of multiplication.
The general rule is that we have to round off each number to its greatest place. General rule for rounding: 1 ) If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 108 rounded to the nearest ten is 110. and nearest hundred = 100.
The Basic Laws of Algebra are the associative, commutative and distributive laws. They help explain the relationship between number operations and lend towards simplifying equations or solving them.
So: The nth term is = 5n - 1.
Detailed Solution
Hence, "option 4" is the correct answer.
Thus , tn=(1)(2)n−1=2n−1. Was this answer helpful?
Therefore, the general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.
Consider 81 and 27. If you subtract 18 from 81 you get 63, not 27. So the pattern rule is "not subtract 18." If you divide 81 by 3 you get 27.
Therefore, nth term is 2n−1.
The nth term of the sequence 1, 1/2, 1/3, 1/4, 1/5 is 1/n.
So, the next term is: 2 × 2 × 2 × 2 × 2 × 2 = 64.