Question

A card is drawn from a well-shuffled pack of 52 playing cards.
the probability that the card drawn is (1) a diamond card (2) a face
(3) a black card
The sum of three consecutive terms of an A.P. is 36 and their product is
Find the terms. (Consider the terms to be in descending order)
forum B MATHEMATICS (PART 1)​

Answer 1

Answer:

Answer

Let a−d,a,a+d be the first three terms of an A.P.

It is given that the sum of the terms is 6 that is:

a−d+a+a+d=6

⇒3a=6

⇒a=

3

6

⇒a=2(1)

It is also given that the product of the terms is −120 that is:

(a−d)(a)(a+d)=−120

⇒a(a

2

−d

2

)=−120(∵(x+y)(x−y)=x

2

−y

2

)

⇒2(2

2

−d

2

)=−120(From(1))

⇒4−d

2

=−

2

120

⇒4−d

2

=−60

⇒d

2

=4+60

⇒d

2

=64

⇒d=±

64

⇒d=±8 (2)

Now, if a=2 and d=−8 then the first three terms of the A.P are:

a−d=2−(−8)=2+8=10

a=2 and

a+d=2−8=−6

And if a=2 and d=8 then the first three terms of the A.P are:

a−d=2−8=−6

a=2 and

a+d=2+8=10

Hence, the three terms are −6,2,10 or 10,2,−6