Write the first three terms of an arithmetic sequence if the fourth term is 10 and D = -6?
Answers
Answer:
First three terms = 28, 22, and 16
Step-by-step explanation:
The formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d, where:
- an is the nth term,
- a1 is the first term,
- n is the term position (e.g., 1st, 4th, etc.),
- and d is the common difference.
Step 1: Find a1:
We can find a1 by substituting 10 for an, 4 for n, and -6 for d in the nth term formula:
10 = a1 + (4 - 1) * -6
10 = a1 + 3 * -6
(10 = a1 - 18) + 18
28 = a1
Thus, the first term is 28.
Step 2: Find a2 (the second term):
Now, we can find the second term by substituting 28 for a1, 2 for n, and -6 for d in the nth term formula:
a2 = 28 + (2 - 1) * -6
a2 = 28 + 1 * -6
a2 = 28 - 6
a2 = 22
Thus, the second term is 22.
Step 3: Find a3 (the third term):
Now, we can find the third term by substituting 28 for a2, 3 for n, and -6 for d in the nth term formula:
a3 = 28 + (3 - 1) * -6
a3 = 28 + 2 * -6
a3 = 28 - 12
a3 = 16
Thus, the third term is 16.
Step 4: Write the first three terms:
Therefore, the first three terms of the arithmetic series are 28, 22, and 16.
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Answers
Hope this helps.
t(4 + 1)
t(5)
5t
What property or properties were used to prove that the expressions are equivalent?
commutative and distributive properties
associative and distributive properties
associative and commutative properties
associative property
Answers
The proof used the distributive property and the associative property of multiplication.
Option B is the correct answer.
What is an expression?
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the liketerms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To be specific, the distributiveproperty was used to break down the expression 4t + t as:
4t + t = (4 + 1)t ________(1)
And then the associativeproperty was used to rearrange the terms as:
(4 + 1)t = 5t ________(2)
From (1) and (2)
We have shown that 4t + t is equivalent to 5t.
Thus,
The proof used the distributive property and the associative property of multiplication.
Learn more about expressions here:
#SPJ2
Answer:
its A: commutative and distributive properties
Step-by-step explanation:
i got it right