What is a1 of the arithmetic sequence for which a3=10 and a51=−182?
1 answer:
Answer:
a₁ = 18
Step-by-step explanation:
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 10 and a₅₁ = - 182, then
a₁ + 2d = 10 → (1)
a₁ + 50d = - 182 → (2)
Subtract (1) from (2) term by term to eliminate a₁
48d = - 192 ( divide both sides by 48 )
d = - 4
Substitute d = - 4 into (1) and evaluate for a₁
a₁ + 2(- 4) = 10
a₁ - 8 = 10 ( add 8 to both sides )
a₁ = 18
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Answer:
<em>4 + 7x – 2</em>
Step-by-step explanation:
<u>Equivalent Expressions</u>
Let's find out which expressions are equivalent by simplifying them. One of the expressions should be not equivalent to the other three.
Simplifying
Now for the second expression
The third expression simplifies to
Finally, this is the simplification for the expression
As seen, the only expression not equivalent to the other three is 4 + 7x – 2