hi guys
please help me out
Answers
Solution :
1.
Question :
If a, b, c are in G.P., then a correct statement is
a) a = bc
b) b² = ac
c) c = ab
d) a² = bc
Answer :
If a, b, c are in G.P. then the correct statement is
Option (b) ↬ b² = ac
2.
Question :
The common ration of 0.04 + 0.02+ 0.01 + ... is
a) 1/2
b) 1/3
c) 2
d) 3
Answer :
The G.P. is 0.04 + 0.02 + 0.001 + ...
So, the common ratio
= (2nd term)/(1st term)
= 0.02 / 0.04
= 0.5
= 1/2
Option (a) ↬ 1/2 is correct
3.
Question :
If the nth term of a G.P. is 2*(0.5)ⁿ⁻¹, then the common ratio is
a) 0.2
b) 5
c) 0.5
d) 2
Answer :
The nth term of the G.P.
= 2*(0.5)ⁿ⁻¹
Then, (n-1)th term of the G.P.
= 2*(0.5)ⁿ⁻²
So, the common ratio
= (nth term) / {(n-1)th term}
= {2*(0.5)ⁿ⁻¹} / {2*(0.5)ⁿ⁻²}
= 1/{(0.5)⁻¹}
= 0.5
Option (c) ↬ 0.5 is correct
4.
Question :
The common ratio of the G.P. 1 - 1/2 + 1/4 - 1/8 + ... is
a) -1/2
b) 1/2
c) -2
d) 3
Answer :
The G.P. is 1 - 1/2 + 1/4 - 1/8 + ...
Then, common ratio
= (-1/2) / (1) = -1/2
= (1/4) / (- 1/2) = -1/2
Option (a) ↬ (-1/2) is correct
5.
Question :
If kᵃ, kᵇ, kᶜ are in G.P., then a, b, c are in
a) H.P.
b) A.P.
c) G.P.
d) can't say
Answer :
Given kᵃ, kᵇ and kᶜ are in G.P.
Then, (kᵇ)² = kᵃ * kᶜ
or, k²ᵇ = kᵃ * kᶜ
Taking (log) to both sides, we get
log(k²ᵇ) = log(kᵃ * kᶜ)
or, 2b logk = a logk + c logk
or, 2b = a + c ,
which prescribes an A.P.
Thus, a, b, c are in A.P.
Option (b) ↬ A.P. is correct
6.
Question :
The nth term of the G.P. 8, 24, 72, 216, ... is
a) 2³ 3ⁿ⁻¹
b) 3² 3ⁿ⁻¹
c) 2³ 3ⁿ
d) 2³ 3ⁿ⁺¹
Answer :
The G.P. is (a =) 8, 24, 72, 216, ...
Common ratio (r) = 24/8 = 3
So, nth term = a * rⁿ⁻¹
= 8 * 3ⁿ⁻¹
= 2³ * 3ⁿ⁻¹
Option (a) ↬ 2³ * 3ⁿ⁻¹ is correct
7.
Question :
The reciprocal of a G.P. is
a) A.P.
b) G.P.
c) H.P.
d) none
Answer :
Reciprocal of a G.P. is a G.P.
Option (b) ↬ G.P. is correct