Question

17,22,27,32..., Determine if the given sequences represent an AP, assuming that the pattern continues. If it is an AP, find the nth term.

Answer 1

nth term=17+(n-1)5
=12+5n

Answer 2

Given sequence :

17 , 22 , 27 ,32 ,...

a2 - a1 = 22 - 17 = 5 ,

a3 - a2 = 27 - 22 = 5

Therefore

a2 - a1 = a3 - a2 = 5

Given sequence is in A.P.

Now ,

First term = a = 17 ,

Common difference (d) = 5

Let number of terms = n

nth term = an = a + ( n - 1 )d

= 17 + ( n -1 )5

= 17 + 5n - 5

= 12 + 5n

Therefore ,

nth term in A.P = n = 5n + 12

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