Question

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

Answer 1

In the given problem, we are given an A.P and the value of one of its term.

We need to find whether it is a term of the A.P or not.

So here we will use the formula, `a_n = a + (n - 1)d`

Here, A.P is 11, 8, 5, 2,....

`a_n = -150`

a = 11

Now

Common difference(d) = `a_1 - a`

= 8 − 11

= −3

Thus, using the above mentioned formula

- 150 = 11 + (n − 1) (−3)

-150 − 11 = −3n + 3

-161 − 3 = −3n

`n = (-164)/(-3)`

Since, the value of n is a fraction.

Thus −150 is not the term of the given A.P. 

Therefore the answer is NO.