Question

What is the 30th term of the linear sequence below? − 5 , − 2 , 1 , 4 , 7 ,

Answer 1

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 2

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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