Series Test

Result

Series Test - 2

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If the p^thterm of an A.P. is q and the q^th term is p, then the r^th term of the A.P. is

A
0

B
p + q + r

C
p + q - r

D
p - q - r

Solution

a + (p - 1) d = q
& a + (q - 1) d = p
d = -1 & a = p + q - 1
Tr = a + (r - 1) d = p + r - 1 + (r - 1) - 1 = p + q - r
Question 2
1 / -0

If x, y, z are in A.P., find the value of (x + 2y - z)(2y + z - x)(z + x -y).

A
xyz

B
2xyz

C
4xyz

D
None of these

Solution

As x, y, z are in A.P, therefore 2y = x + z
The given expression is (x + 2y – z)(2y + z – x)(z + x – y).
= (x + x + z – z) (x + z + z – x) (2y – y)
= 2x ´ 2z ´ y = 4xyz
Question 3
1 / -0

If the 5th, 8th and 11th terms of a G.P. are p, q and s respectively, then

A
q = ps

B
q² = ps

C
q³ = ps

D
None of these

Solution

ar⁴ = p, ar⁷ = q and ar¹⁰ = s
ps = (ar⁴) (ar¹⁰) = (a² r¹⁴) = (ar⁷)² = q²
Question 4
1 / -0

If x, 2x + 2, 3x + 3 are in a GP, then the fourth term is

A
– 27

B
27

C
– 13.5

D
13.5

Solution

x, 2x + 2, 3x + 3 are in a GP.
(2x + 2)² = 3(x + 1) x
4 (x + 1) = 3x ⇒ x = – 4
So, the terms are – 4, – 6, – 9.
a = – 4 and r = 3/2
Fourth term = ar³ ⇒ – 27/2 = – 13.5