Practice Questions for Algebra - Progressions | CRE 2

1. CRE 2 - Geometric Progression | Algebra - Progressions

In G.P. of 100 numbers if 13^th term from the beginning is 50, find the 88^th term from the end.

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7 8 9 4 5 6 1 2 3 0 . -

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2. CRE 2 - Geometric Progression | Algebra - Progressions

The numbers (√3 + 1), √2, (√3 - 1) will be in

(a)
A.P.
(b)
G.P.
(c)
H.P.
(d)
None of these

3. CRE 2 - Geometric Progression | Algebra - Progressions

Product of three numbers in G.P. is 512. Find the second number.

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4. CRE 2 - Geometric Progression | Algebra - Progressions

The sum of first two terms of a G.P. is 2 and every term of this series is thrice of its previous term, then the first term will be

(a)
1/4
(b)
1/3
(c)
2/3
(d)
1/2

5. CRE 2 - Geometric Progression | Algebra - Progressions

The second term of geometric sequence is 3 and the 50^th term is 81/8. The 98^th term of the sequence is:

(a)
21///64
(b)
2187/63
(c)
2188/63
(d)
2187/64

6. CRE 2 - Geometric Progression | Algebra - Progressions

If the 6^th term of the G.P. is 2, then the product of first 11 terms is

(a)
1024
(b)
512
(c)
2048
(d)
None of these

7. CRE 2 - Geometric Progression | Algebra - Progressions

The first and last terms of a G.P. are a and l respectively; r being its common ratio; then the number of terms in this G.P. is

(a)
(log l - log a)/log r
(b)
1 - (log l - log a)/log r
(c)
(log a - log l)/log r
(d)
1 + (log l - log a)/log r

8. CRE 2 - Geometric Progression | Algebra - Progressions

If a, b, c are in G.P., then log a, log b, log c are in

(a)
A.P.
(b)
G.P.
(c)
H.P.
(d)
Cannot be determined

9. CRE 2 - Geometric Progression | Algebra - Progressions

Find the total number of terms in a G.P., if its first term is 12, last term is 2916 and the common ratio is 3.

(a)
5
(b)
6
(c)
8
(d)
10
(e)
12

10. CRE 2 - Geometric Progression | Algebra - Progressions

Product of the first and fifth term of a G.P. is 1296. Find the third term.

(a)
36
(b)
6
(c)
12
(d)
24
(e)
32

11. CRE 2 - Geometric Progression | Algebra - Progressions

Sum of all odd terms of a GP containing 100 terms is 1122 and the sum of all even terms of the same GP is 1683. Find the common ratio.

(a)
2
(b)
2/3
(c)
3/2
(d)
1/2

Answer: Option C

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Explanation :

Sum of odd terms of a GP with first term a and common ratio = r is
a + ar² + ar⁴ + ar⁶ + … + ar⁹⁸ = 1122 …(1)

Sum of even terms of a GP with first term a and common ratio = r is
ar + ar³ + ar⁵ + ar⁷ + … + ar⁹⁹ = 1683 …(2)

Dividing (2) by (1),
$\frac{a r + a r^{3} + a r^{5} + a r^{7} + \dots + a r^{99}}{a + a r^{2} + a r^{4} + a r^{6} + \dots + a r^{98}}$ = $\frac{1683}{1122}$

∴ $\frac{a r (1 + r^{2} + r^{4} + a r^{6} + \dots + a r^{98})}{a (1 + r^{2} + r^{4} + r^{6} + \dots + a r^{98})}$ = $\frac{3}{2}$

∴ r = $\frac{3}{2}$

Hence, option (c).

12. CRE 2 - Geometric Progression | Algebra - Progressions

If a, b, c and d are in GP, then (a + b), (b + c) and (c + d) are in

(a)
AP
(b)
GP
(c)
HP
(d)
Cannot be determined

13. CRE 2 - Geometric Progression | Algebra - Progressions

a, b & c are in G.P. and $\sqrt[p]{a}$ = $\sqrt[q]{b}$ = $\sqrt[r]{c}$ . p, q and r are in

(a)
AP
(b)
GP
(c)
HP
(d)
None of these

Answer: Option A

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Explanation :

Let $\sqrt[p]{a}$ = $\sqrt[q]{b}$ = $\sqrt[r]{c}$ = k

⇒ a = k^p, b = k^q anc c = k^r.

since, a, b and are in GP

⇒ a × c = b²

⇒ k^p × k^r = (k^p)²

⇒ k^p+r = k^2p

∴ p + r = 2p

∴ p. q and r are in AP.

Hence, option (a).

CRE 2 - Geometric Progression | Algebra - Progressions

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