What is the 13th term of the following sequence -3, - 1/2, 2, ......?

Question: What is the 13th term of the following sequence -3, - 1/2, 2, ......?

Solution:
This is an arithmetic progression (AP) because the difference between consecutive terms is constant.
Here,
First term (a) = - 3
Common difference (d) = - (1/2) - (-3) = - 0.5 + 3 = 2.5
Number of terms (n) = 13

We know the formula for the n^th term is:
a_n = a + (n - 1)d

So, the 13^th term is:
a₁₃ = - 3 + (13 - 1) × 2.5
⇒ a₁₃ = - 3 + (12 × 2.5)
⇒ a₁₃ = - 3 + 30
∴ a₁₃ = 27

So, the 13th term of the sequence is 27.