Question
Find:
Is $-150$ a term of the$ A.P. 11, 8, 5, 2, .....?$
Is $-150$ a term of the$ A.P. 11, 8, 5, 2, .....?$
✓
Answer
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 $11, 8, 5, 2, .....$
$a_n = -150, a = 11$ and $d = 8 - 11 = -3$
Thus, using the above mentioned formula, we get
$- 150 = 11 + (n - 1)(-3)$
$\Rightarrow -150 - 11 = -3n + 3$
$\Rightarrow -161 = -3n + 3$
$\Rightarrow -161 - 3 = -3n$
$\Rightarrow -3n = -164$
$\Rightarrow\ \text{n}=\frac{164}{3}$
Since, the value of n is a fraction. Thus, $-150$ is not the term of the given $A.P.$
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 $11, 8, 5, 2, .....$
$a_n = -150, a = 11$ and $d = 8 - 11 = -3$
Thus, using the above mentioned formula, we get
$- 150 = 11 + (n - 1)(-3)$
$\Rightarrow -150 - 11 = -3n + 3$
$\Rightarrow -161 = -3n + 3$
$\Rightarrow -161 - 3 = -3n$
$\Rightarrow -3n = -164$
$\Rightarrow\ \text{n}=\frac{164}{3}$
Since, the value of n is a fraction. Thus, $-150$ is not the term of the given $A.P.$
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