What's the 30th of the linear sequence

-5,-2,1,4,7

The 30th term of the given sequence is 82.

Step-by-step explanation:

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. The given linear sequence (-5,-2,1,4,7) is in the form of Arithmetic Progression with a common difference of 3. - 5, - 5+3 = - 2, - 2+3 = 1, 1+3 = 4 and so on.

The nth term is given by the formula nth term = a + (n - 1) d

where

a = first term

d = common difference

To find the 30th term in the given sequence:

The first term, a = - 5 and the common difference, d = 3.

30th term = - 5 + (30-1) 3

⇒ - 5 + (29) 3

⇒ - 5 + 87

⇒ 82

Therefore, the 30th term in the given sequence is 82.