Question
Is $-150$ a term of $11, 8, 5, 2,$ .......?
✓
Answer
The given sequence is 11, 8, 5, 2, …..
Now,
8 - 11 = 5 - 8 = 2 - 5 = -3
Hence, the given sequence is an A.P. with first term a = 11 and common difference d = -3.
The general term of an A.P. is given by
$t_n = a + (n - 1)d$
$\Rightarrow -150 = 11 + (n - 1)(-3)$
$\Rightarrow -161 = -3n + (-3)$
$\Rightarrow 3n = 164$
$\Rightarrow n=\frac{164}{3}$
The number of terms cannot be a fraction.
So, clearly, -150 is not a term of the given sequence.
Now,
8 - 11 = 5 - 8 = 2 - 5 = -3
Hence, the given sequence is an A.P. with first term a = 11 and common difference d = -3.
The general term of an A.P. is given by
$t_n = a + (n - 1)d$
$\Rightarrow -150 = 11 + (n - 1)(-3)$
$\Rightarrow -161 = -3n + (-3)$
$\Rightarrow 3n = 164$
$\Rightarrow n=\frac{164}{3}$
The number of terms cannot be a fraction.
So, clearly, -150 is not a term of the given sequence.
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