Advertisements
Advertisements
प्रश्न
If a, b, c is three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that xb–c × yc–a × za–b = 1
उत्तर
a, b, c is three consecutive terms of an AP.
∴ Let a, b, c be a, a + d, a + 2d respectively ...(1)
x, y, z is three consecutive terms of a GP.
∴ Assume x, y, z as x, x.r, x.r2 respectively ...(2)
PT : xb–c, yc–a, za–b = 1
Substituting (1) and (2) in L.H.S., we get
L.H.S. = `x^("a" + "d" - "a" - 2"d") xx (x"r")^("a" + 2"d" - "a") xx (x"r"^2)^("a" - "a" - "d")`
= (x)–d . (xr)2d (xr2)–d
= `1/x^4 xx x^(2"d") * "r"^(2"d") xx 1/(x^"d" "r"^(2"d")` = 1 = R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Identify the following sequence is in G.P.?
0.5, 0.05, 0.005, …
Identify the following sequence is in G.P.?
`1/3, 1/6, 1/12, ...`
Identify the following sequence is in G.P.?
1, −5, 25, −125, ...
Write the first three terms of the G.P. whose first term and the common ratio are given below
a = 6, r = 3
Write the first three terms of the G.P. whose first term and the common ratio are given below
a = `sqrt(2)`, r = `sqrt(2)`
A man joined a company as Assistant Manager. The company gave him a starting salary of ₹ 60,000 and agreed to increase his salary 5% annually. What will be his salary after 5 years?
For a GP, if Sn = `(4^"n" - 3^"n")/3^"n"`, then t2 = _______.
For a GP, if (m + n)th term is p and (m - n)th term is q, then mth term is _____.
For a sequence (tn), if Sn = 5(2n - 1) then tn = ______.
If A, B, C are pth, qth and rth terms of a GP respectively then Aq - r · Br - p · Cp - q = ______.
