Question

In A.P $ 11,8,5,2,...... $ . which term is the number $ ... - 151 $ ?

Answer 1

Hint: To solve this problem we make use of the following formulae,
The $ {n^{th}} $ term of an A.P will be given by,
 $ {a_n} = a + \left( {n - 1} \right)d $
Here,
 $ {a_n} $ , will be the $ {n^{th}} $ of an A.P
 $ d $ , will be the common difference
 $ n $ , will be the number of terms
 $ a $ , will be the first term

Complete step-by-step answer:
So we have the sequence of an arithmetic progression, which is $ 11,8,5,2,...... $
To solve it, now we have to find the term where this number $ - 151 $ belongs to. So for this, we will use the formula of $ {n^{th}} $ the term of an A.P.
We have the formula which is $ {a_n} = a + \left( {n - 1} \right)d $
On comparing the finding the values from the A.P series, we have
 $ {a_n} = - 151 $
 $ d = 8 - 11 = - 3 $
 $ a = 11 $
So on substituting the values in the formula we have the equation,
 $ \Rightarrow - 151 = 11 + \left( {n - 1} \right)\left( { - 3} \right) $
Now on solving the braces, we get
 $ \Rightarrow - 151 = 11 - 3n + 3 $
Now taking the constant term to one side and we will find the values for $ n $
 $ \Rightarrow - 3n = - 165 $
On dividing the above equation, we will get the values as
 $ \Rightarrow n = \dfrac{{165}}{3} $
And we get the value as
 $ \Rightarrow n = 55 $
So, $ - 151 $ will be the $ {55^{th}} $ term of the given arithmetic progression.
So, the correct answer is “ $ {55^{th}} $”.

Note: For solving this type of question we just need to memorize the formula and then we can easily solve it. One more thing we should keep in mind that while taking the values from the series, we also have to consider the sign. So while taking it we should be careful.