HARD
11th ICSE
IMPORTANT
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Three numbers whose sum is 70 are in G.P. If each of the extremes is multiplied by 4 and the mean by 5, the numbers will be in A.P. Find the numbers.

Important Questions on Sequences and Series

HARD
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 23
There are four numbers such that first three of them form an arithmetic sequence and the last three form a geometric sequence. The sum of the first and third number is 2 and that of second and fourth is 26. What are these numbers?
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 24
If a,b,c are in A.P. as well in G.P., prove that a=b=c.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 24
If a,b,c are in A.P. as well as in G.P., then find the value of ab-c+bc-a+ca-b.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 25
The terms of a G.P. with first term a and common ratio r are squared. Prove that resulting sequence is also a G.P. Find its first term, common ratio and the nth term.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 26
If a,b,c are in G.P. show that 1a,1b,1c are also in G.P.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 26
If K is any positive real number and Ka,Kb,Kc are three consecutive terms of a G.P., prove that a,b,c are three consecutive terms of an A.P.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 26
If p, q, r are in A.P., show that pth, qth and rth terms of any G.P. are themselves in G.P.
MEDIUM
11th ICSE
IMPORTANT
Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.5>Q 27
If a, b, c are in G.P., prove that a3,b3,c3  are also in G.P.