What is the 30th term of the linear sequence below? − 5 , − 2 , 1 , 4 , 7 ,
Answers
Step-by-step explanation:
Let a is first term and d is common difference.
nth term = a + (n-1)d
In question,
a = - 5
d = - 2 - ( - 5 ) = - 2 + 5 = 3
So,
=> 30th term is
=> -5 + (30-1)(3)
=> - 5 + (29)3
=> - 5 + 87
=> 82
Answer:
The 30th term of the sequence -5, -2, 1, 4, 7 is 82.
Step-by-step explanation:
Given:
Sequence: -5, -2, 1, 4, 7
To find:
30th term (a₃₀) =?
Formula:
nth term = a₁ + (n-1)d
Solution:
Step 1: To find the common difference
The given sequence is -5, -2, 1, 4, 7.
So, a₁ = -5, a₂ = -2, a₃ = 1, a₄ = 4, and a₅ = 7.
To find the common difference, we subtract the consecutive terms.
a₂ - a₁ = -2 - (-5) = -2 + 5 = 3
a₃ - a₂ = 1 - (-2) = 1 + 2 = 3
a₄ - a₃ = 4 - 1 = 3
a₅ - a₄ = 7 - 4 = 3
Since the difference between all two consecutive terms is the same, the given sequence is an arithmetic progression.
Common difference (d) = a₂ - a₁
Common difference (d) = -2 -(-5)
Common difference (d) = -2 + 5
Common difference (d) = 3
Step 2: To find the 30th term
The formula to find the nth term of an arithmetic progression is as follows:
nth term = a₁ + (n-1)d
where a₁ is the first term and d is the common difference.
Substituting the given values, we get
a₃₀ = -5 + (30-1)3
a₃₀ = -5 + (29)3
a₃₀ = -5 + 87
a₃₀ = 82
Therefore, the 30th term of the given linear sequence is 82.
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