Question

check weather -150 is a term of the AP 11,8,5,2.

Answer 1

Solution:

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Given:

AP: 11,8,5,2.

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To verify:

 -150 is a term in the given AP,.

To find a value for n (where n is a natural number)
 
 $a_n = -150$

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As we know,

AP: 11,8,5,2..

a =11,

$d= a_2 - a_1 = 8-11=-3$

$a_n = -150$


We know that,

$a_n = a+(n-1)d$

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

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

$-161 -3 =-3n$

[tex]-164 = -3n [/tex]

$n= \frac{164}{3}$

    ∴n = 54.67

And hence,

n is not a natural number (it has values in decimals)

So,

-150 is not in the given AP,.

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                                            Hope it Helps !!

Answer 2

☺ Hello mate__ ❤

◾◾here is your answer...

Let −150 is the nth of AP 11,8,5,2...     

which means that  an'=−150

Here, First term = a = 11

Common difference = d = 8 - 11 = -3

Using formula an'=a+(n−1)d,  

to find nth term of arithmetic progression, we get

−150=11+(n−1)(−3)

⇒−150=11−3n+3

⇒3n=164

⇒n=164/3

But, n cannot be in fraction. Therefore, our supposition is wrong. −150 cannot be term in AP.

I hope, this will help you.

Thank you______❤

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