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