Question

Decide whether following sequence is an A.P., if so find the 20th 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,
a20=a+n-1d      =-12+20-17      =-12+197      =121">a20=a+(n−1)d      =−12+(20−1)7      =−12+(19)7      =121

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