Question

check whether - 120 is a term of the AP :11,8,5,2 ....​

Answer 1

Answer:

first term, a=11

common difference, d= 8-11

= -3

let -120 be nth term of this AP

an = a + (n-1)d

-120=11+(n-1)(-3)

-120-11= -3n+3

-131= -3n+3

3n=131+3

3n=134

n=134/3

n is not a whole number

so -120 is not a term of this AP

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Answer 2

We recall that, $a_n$ the term an A.P.

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

Given: An A.P. $11,8,5,2,....$

First-term, $a=11$

Common Difference d,

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

$a_n=-120$

$-120=11+(n-1)(-3)\\-120-11=(n-1)(-3)\\-131=(n-1)(-3)\\\frac{131}{3}=n-1\\n=\frac{131}{3}+1\\n=\frac{134}{3}$

The value $n$ should be a natural number.

$-120$ is not part of an AP.