Advertisements
Advertisements
प्रश्न
If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.
Show that : x2, b2, y2 are in A.P.
Advertisements
उत्तर
a, b and c are in A.P.
`=>` 2b = a + c
a, x and b are in G.P.
`=>` x2 = ab
b, y and c are in G.P.
`=>` y2 = bc
Now,
x2 + y2 = ab + bc
= b(a + c)
= b × 2b
= 2b2
`=>` x2, b2 and y2 are in A.P.
संबंधित प्रश्न
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Find the geometric progression with 4th term = 54 and 7th term = 1458.
If for a G.P., pth, qth and rth terms are a, b and c respectively; prove that : (q – r) log a + (r – p) log b + (p – q) log c = 0
Q 8
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Find the sum of G.P. : 3, 6, 12, .........., 1536.
The sum of three numbers in G.P. is `39/10` and their product is 1. Find the numbers.
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
