The 30th term of the given sequence is 82.
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.