Question

Find the number of terms in the series 11,6,1,...,-54

Answer 1

Answer :

14th term

Explanation:

Given sequence 11,6,1,...,-54

a2-a1= 6-11 = -5

a3-a2 = 1-6 = -5

a2-a1 = a3-a2 = -5

Given sequance is in A.P.

Now ,

first term (a) = 11,

common difference (d)=-5

Let nth term = -54

=> a+(n-1)d=-54

=> 11+(n-1)(-5)=-54

=> (n-1)(-5)=-54-11

=> (n-1)(-5) = -65

=> n-1 = (-65)/(-5)

=> n-1 = 13

=> n = 13+1

=> n = 14

Therefore,

14th term in an A.P. = -54

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