Question

Find whether zero is a term of A.P 40,37,34,31....​


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Answer 1

$\huge{\bold{SOLUTION:-}}$

Given terms :

= 40,37,34,31,...

Here,

First term=a=40

and, common difference=d= -3

Let the nth term be 0

→a+(n-1)d=0

→40+(n-1)(-3)=0

→40-3n+3=0

→3n=43

→n=43/3

Here , n can't be a fraction for any value of nth term

Here , n can't be a fraction for any value of nth termSo , zero isn't a term of the given term

Answer 2

Given AP :- 40, 37, 34, 31...

here.

• a (first term) = 40

• d (common difference) = a2 - a1 = 37 - 40 = -3

now, we've to check whether 0 is a term of the given AP or not.

let us suppose that 0 is a term of the given AP. let us denote as nth term of the AP.

we know that,

an = a + (n - 1)d

⇒ 0 = 40 + (n - 1)-3

⇒ 0 = 40 + (-3n + 3)

⇒ 0 = 40 - 3n + 3

⇒ 0 = 43 - 3n

⇒ 3n = 43

⇒ n = 43/3

∵ n = 43/3 which is in fraction and we know that terms can'be in fraction.

∴ 0 isn't a term of the give AP.