Question

p, q, r, s, t are the first five terms of the A. P such that p +r +t = -12 and pqr =8. Find the first term of the A. P

Answer 1

Let the common difference be d.

So, p = r-2d , q=r-d , r=r , s=r+d , t=r+2d

Hence,

From first equation, we get,

r= -4

Also,

Find the value of d by putting in second equation.

Afterwards, get the first term of A.P.

Answer 2

Answer: the first term is 2

Step-by-step explanation:

Given: p, q. r, s, t are in AP

Let d is the common difference

Therefore

p = a-2d, q= a-d, r=a, s=a+d, t= a+2d

As given p+r+t = - 12

a-2d+a+a+2d= -12

3a= -12

a= -4

Now

pqr= 8

(a-2d)(a-d)(a)= 8

⇒ (-4-2d)(-4-d)(-4)=8

⇒(-2)(2+d)(-1)(4+d)(-4) = 8

⇒ (2+d)(4+d) = -1

⇒ 8+2d+4d+d² = -1

⇒d²+6d+9=0

⇒ d²+ 3d+3d+9=0

⇒d(d+3)+3(d+3)=0

⇒d+3=0

⇒ d= -3

First term is a-2d = -4-2(-3) = -4+6 = 2

Hence, the first term is 2