Question

Find the first negative term from following A.P 122,116,110

Answer 1

Answer:

$\bigstar{\bold{First\:negative\:term=-4}}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• A.P is 122, 116, 110...

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The first negative term

$\Large{\underline{\underline{\it{Solution:}}}}$

→ First we have to find the common difference (d) of the A.P

  d = a₂ - a₁

  where a₂ = 116, a₁ = 122

→ Substituting the datas, we get

  d = 116 - 122

  d = -6

→ Let $a_n$ th term be the first negative term which is given by,

  $a_n=a_1+(n-1)\times d$

→ So, $a_n<0$

→ Hence,

  $a_1+(n-1)\times d<0$

→ Substituting the datas we get,

  $122+(n-1)\times -6<0$

 $-6n+6<-122$

 $-6n<-122-6$

   $6n>128$

    $n>\dfrac{128}{6}$

   $n>21.33$

→ Hence the 22nd term is negative.

→ The formula for finding 22nd term of an A.P is given by

  a₂₂ = a₁ + ( 22-1) × d

→ Substitute the datas,

  a₂₂ = 122 + 21 × -6

  a₂₂ = 122 -126

  a₂₂ = -4

→ Hence the first negative term is -4.

$\boxed{\bold{First\:negative\:term=-4}}$

$\Large{\underline {\underline{\it{Notes:}}}}$

→ The nth term of an A.P is given by

   $a_n=a_1+(n-1)\times d$

Answer 2

Answer:

$\bigstar{\bold{First\:negative\:term=-4}}$★Firstnegativeterm=−4

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

Given:

A.P is 122, 116, 110...

$\Large{\underline{\underline{\it{To\:Find:}}}}$

The first negative term

$\Large{\underline{\underline{\it{Solution:}}}}$

→ First we have to find the common difference (d) of the A.P

d = a₂ - a₁

where a₂ = 116, a₁ = 122

→ Substituting the datas, we get

d = 116 - 122

d = -6

→ Let a_na

n

th term be the first negative term which is given by,

a_n=a_1+(n-1)\times da

n

=a

1

+(n−1)×d

→ So, a_n<0a

n

<0

→ Hence,

a_1+(n-1)\times d<0a

1

+(n−1)×d<0

→ Substituting the datas we get,

122+(n-1)\times -6<0122+(n−1)×−6<0

-6n+6<-122−6n+6<−122

-6n<-122-6−6n<−122−6

6n>1286n>128

$n>\dfrac{128}{6}n>$

6

128

n>21.33n>21.33

→ Hence the 22nd term is negative.

→ The formula for finding 22nd term of an A.P is given by

a₂₂ = a₁ + ( 22-1) × d

→ Substitute the datas,

a₂₂ = 122 + 21 × -6

a₂₂ = 122 -126

a₂₂ = -4

→ Hence the first negative term is -4.

$\boxed{\bold{First\:negative\:term=-4}}$

Firstnegativeterm=−4

$\Large{\underline {\underline{\it{Notes:}}}}$

→ The nth term of an A.P is given by

a_n=a_1+(n-1)\times da

n

=a

1

+(n−1)×d