Question

Check whether -150 is a term of the AP 11,8,5,2,••••
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Answer 1

Step-by-step explanation:

In APs, nth term = a + ( n - 1 )d, a is first term and d is common difference.

Here,

First term = 11

Com. Dif. = 8 - 11 = - 3

If - 150 is in AP, let it be nth term of AP.

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

= > (n - 1)(-3) = - 150 - 11 = - 161

= > n - 1 = - 161/(-3) = 161/3

= > n - 1 = 53.6

= > n = 54.6

As n is a decimal number, - 150 is not in this AP.

Answer 2

a = 11

d = 8-11 = -3

Let aₙ = -150

∴ If n is a positive integer then -150 will be the term of the AP.

aₙ = a + (n-1) d = -150

a + (n-1) d = -150

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

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

-3(n-1) = -161

n-1 = -161/-3

n-1 = 53.67

n = 53.67+1

n = 54.67

As n ≠ positive integer, therefore -150 is not a term of the AP = 11,8,5,2,...