Question

1 -if the 9 th term of an A.P is zero then show that the 29 th term is twice the 19 th term
2- A die is rolled .find the probability that 1) a number greater than 2 comes up. 2) a number multiple of 2
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Answer 1

Question no. 1

To prove:  $a+28d=2(a+18d)$

$a+(9-1)d=0\\a+8d=0\\a=(-8d)$

Substituting the value of "a" in the question:

$LHS:\\\\a+28d=28d-8d=20d$

$RHS:\\2(a+18d)=2(18d-8d)=2(10d)=20d$

LHS = RHS, thus proved.

Question no. 2

1) Probability of a number greater than two being rolled on the dice:

$\frac{(3,4,5,6)}{(1,2,3,4,5,6)} = \frac{4}{6}= \frac{2}{3}$

2) Probability of a multiple of two being rolled on the dice:

$\frac{(2,4,6)}{(1,2,3,4,5,6)} = \frac{3}{6} = \frac{1}{2}$