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

Given A.P. is – 12, – 5, 2, 9, 16, 23, 30, . . .

Where first term a = – 12

Second term t1 = – 5

Third term t2 = 2

Common Difference d = t2 – t1 = 2 – ( – 5) = 2 + 5 = 7

We know that, nth term of an A.P. is

tn = a + (n – 1)d

We need to find the 20th term,

Here n = 20

Thus, t20 = – 12 + (20 – 1)× 7

t20 = – 12 + (19)× 7 = – 12 + 133 = 121

Thus, t20 = 121

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