Question

Is–150 a term of the A. P. 11,8,5,2,......?

Answer 1

Let a be the first term and d be the common difference.

Given first term a = 11.

Common difference d = 8 - 11

                                      = -3.

Given an = -150.


We know that sum of n terms of an AP an = a + (n - 1) * d

                                                                 -150 = 11 + (n - 1)(-3)

                                                                 -150 = 11 - 3n + 3

                                                                 -150 = 14 - 3n

                                                                -164 = -3n

                                                                 n = 164/3

                                                                 n = 54.6.

Clearly,n is not an integer.

Therefore -150 is not a term of this AP.


Hope this helps!

Answer 2

check whether the n comes any natural no. or not if it's is in decimal then it not come in the ap
- 150 = a + (n-1)d
-150 = 11+(n-1) × - 3
-150 -11 = (n-1) ×-3
-161÷-3=(n-1)
53.66 = (n-1)
n= 53.66+1
as n is in decimal so it not come in ap
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