Question

there are 5 constructive terms in ap the product of the first and last term is 189 if the term os9 less than 4yerm​

Answer 1

Answer:

The required A.P is

9, 12, 15, 18, 21 (or) -21, -18, -15, -12, -9

Step-by-step explanation:

Concept:

The n th term of A.P a, a+d, a+2d,....... is

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

Let the 5 consecutive terms of A.P be

a, a+d, a+2d, a+3d, a+4d

As per given data,

Product of first and last term = 189

a(a+4d)=189............(1)

Also,

$t_1=t_4-9\\\\a=a+3d-9\\\\3d=9\\\\d=3$

put d=3 in (1) we get

$a(a+4(3))=189\\\\a^2+12a-189=0\\\\(a+21)(a-9)=0\\\\a=9\:or\:a=-21$

When a=9

The required A.P is

9, 12, 15, 18, 21

when a=-21

The required A.P is

-21, -18, -15, -12, -9