# IIT Foundation Mathematics Problems on Sequence and Series Based on Geometric Progression (G.P.)

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

Q.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

Q.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

Q.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

Q.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

Q.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

Q.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

Q.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

Q.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

Q.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