Question

which term of the sequence -32, -28, -24 is the first positive term

Answer 1

Answer:

$\bigstar{\bold{First\:positive\:term=8th\:term}}$

Step-by-step explanation:

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

• A.P is -32, -28, -24

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

• The first positive term of the sequence

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

→ First we need to find out the common difference of the A.P

  d = a₂ - a₁

  d = -28 + 32

  d = 4

→ Since the term to be found out is positive n > 0

→ The n th term is given by the equation

   $a_n$ = a₁ + (n - 1) d

   a₁ + (n - 1)d > 0

   -32 + ( n - 1 ) 4 > 0

     n = 32/4

     n = 8

→ Therefore the 8th term of the A.P is the first positive term

$\boxed{\bold{First\:positive\:term=8th\:term}}$

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

→ The nth term of an A.P is given by

   $a_n=a_1+(n-1)d$

→ The common difference of an A.P is the difference between its two consecutive terms

d = a₂ - a₁