Question

Decide whether following sequence is an A.P., if so find the 20^th term of the progression.
–12, –5, 2, 9, 16, 23, 30,...

Answer 1

The given sequence is –12, –5, 2, 9, 16, 23, 30,...

Here,
First term (a) = a₁ = –12
Second term = a₂ = –5
Third term = a₃ = 2

Common difference (d) = a₂ – a₁ = –5 – (–12) = 7
= a₃ – a₂ = 2 – (–5) = 7

Since, a₂ – a₁ = a₃ – a₂

Hence, the given sequence is an A.P.

Now,
$$\begin{gathered} a_{20}=a+\left(n-1\right)d \\ =-12+\left(20-1\right)7 \\ =-12+\left(19\right)7 \\ =121 \end{gathered}$$

Hence, the 20^th term of the progression is 121.