Question

Check whether - 150 is a term of the AP 11 , 8 , 5 , 2

Content Quality answer required .​

Answer 1

Here,a=11,d=8−11=−3

Let −150 be the nth term of the given A.P.

We know that,a

n

=a+(n−1)d

−150=11+(n−1)×−3

−150=11−3n+3

(−150)+(−14)=−3n

−3n=−164

3n=164

n=

3

164

So,it is clear that n is not an integer.

Therefore,−150 is not a term of the given A.P.

❥︎hope it helps u

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

Given :

AP 11,8,5,2.........

To Find :

nth term

To Check :

whether -150 is a term of the given AP or not .

Come to the question:

=>Let us assume that it is nth term of AP

so,

$\bold{\boxed{a_{n} = a + (n - 1)d}}$

From given AP

$a_{1}=11\:\&\: a_{2}=8$

$\bold{\boxed{{D=a_{2}-a_{1}}}}$

D=8-11= -3

$\bold{a_{n} = a + (n - 1)d}$

$= > - 150 = 11 + (n - 1) \times - 3$

$= > - 150 = 11 + n( - 3) - 1( - 3)$

$= > - 150 = 11 - 3n + 3$

$= > - 150 = 14 - 3n$

$= > - 150 - 14 = - 3n$

$= > - 164 = - 3n$

$= > n = \frac{ - 164}{ - 3} = 54.33$

$\bold{\red{n = 54.33}}$

Here,we see that n is coming in decimal form.so, it cannot be a term.

$\therefore$-150 is not the term of the given AP.