IIT Foundation Mathematics Problems are helpful for students aspiring for NTSE, Olympiad, KVPY, IIT JEE and other engineering and competitive exams. These questions are prepared by best faculties from all over India.
Here we are providing problems on Sequence and Series based on topic Geometric Progression (G.P.).
Q.1. If 1, x, y, z, 16 are in G.P., then what is the value of x + y + z?
(a) 8
(b) 12
(c) 14
(d) 16
Answer
Answer: cQ.2. If the first term of a G.P. is 729 and its 7th term is 64, then the sum of the first seven terms is
(a) 2187
(b) 2059
(c) 1458
(d) 2123
Answer
Answer: bQ.3. If the third term of a G.P. is 3, then the product of its first 5 terms is:
(a) 15
(b) 81
(c) 243
(d) Cannot be determined
Answer
Answer: cQ.4. If x, 2x + 2, 3x + 3, are the first three terms of a G.P, then the fourth term is
(a) -27/2
(b) 27/2
(c) -33/2
(d) 33/2
Answer
Answer: aQ.5. If 64, 27 and 36 are the Pth, Qth and Rth terms of a G.P, then P + 2Q is equal to
(a) R
(b) 2R
(c) 3R
(d) 4R
Answer
Answer: cQ.6. If a, b, c are unequal numbers such that a, b, c are in A.P. and b – a, c – b, a are in G.P, then a : b : c is
(a) 1 : 2 : 3
(b) 1 : 2 : 4
(c) 1 : 3 : 4
(d) 2 : 3 : 4
Answer
Answer: aQ.7. The first two terms of a geometric progression add upto 12. The sum of the third and fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
(a) – 4
(b) – 12
(c) 12
(d) 4
Answer
Answer: bQ.8. If a, b, c, d are in G.P, then (a + b + c + d)2 is equal to
(a) (a + b)2 + (c + d)2 + 2(b + c)2
(b) (a + b)2 + (c + d)2 + 2(a + c)2
(c) (a + b)2 + (c + d)2 + 2(b + d)2
(d) (a + b)2 + (c + d)2 + (b + c)2
Answer
Answer: aQ.9. The first term of an infinite G.P. is x and its sum is 5. Then,
(a) – 10 < x < 0
(b) 0 < x < 10
(c) 0 ≤ x ≤ 10
(d) x > 10
Answer
Answer: bQ.10. In a G.P, t2 + t5 = 216 and t4 : t6 = 1 : 4 and all the terms are integers, then its first term is
(a) 16
(b) 14
(c) 12
(d) None of these
