General Term | MCQs

Explanation

Let's analyze the sequence:

-5, 7, 19, 31

The differences between consecutive terms are:

7 - (-5) = 12

19 - 7 = 12

31 - 19 = 12

The sequence has a common difference of 12.

The general term for an arithmetic sequence is:

aₙ = a₁ + (n - 1)d

where a₁ is the first term (-5) and d is the common difference (12).

aₙ = -5 + (n - 1)12

aₙ = -5 + 12(n - 1)

Explanation

an = 5n − 7

This is an arithmetic sequence with first term a = -2 and common difference d = 5.

General formula: an = a + (n−1)d = -2 + (n−1)×5 = 5n − 7.