Advertisements
Advertisements
प्रश्न
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(("n" + 1)("n" + 2))/(("n" + 3)("n" + 4))`
Advertisements
उत्तर
Given nth term an = `(("n" + 1)("n" + 2))/(("n" + 3)("n" + 4))`
a1 = `((1 + 1)(1 + 2))/((1 + 3)(1 + 4))`
= `(2*3)/(4*5)`
= `6/20`
= `3/10`
a2 = `((2 + 1)(2 + 2))/((2 + 3)(2 + 4))`
= `(3*4)/(5*6)`
= `12/30`
= `2/5`
a3 = `((3 + 1)(3 + 2))/((3 + 3)(3 + 4))`
= `(4*5)/(6*7)`
= `20/42`
= `10/21`
a4 = `((4 + 1)(4 + 2))/((4 + 3)(4 + 4))`
= `(5*6)/(7*8)`
= `30/56`
= `15/28`
a5 = `((5 + 1)(5 + 2))/((5 + 3)(5 + 4))`
= `(6*7)/(8*9)`
= `42/72`
= `7/12`
a6 = `((6 + 1)(6 + 2))/((6 + 3)(6 + 4))`
= `(7*8)/(9*10)`
= `56/90`
= `28/45`
∴ The given sequece is `3/10, 2/5, 10/21, 15/28, 7/12, 28/45`.
This is neither A.P, G.P nor AGP
APPEARS IN
संबंधित प्रश्न
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`4 (1/2)^"n"`
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(- 1)^"n"/"n"`
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(2"n" + 3)/(3"n" + 4)`
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(3"n" - 2)/(3^("n" - 1))`
Write the first 6 terms of the sequences whose nth term an is given below
an = `{{:(1, "if n" = 1),(2, "if n" = 2),("a"_("n" - 1) + "a"_("n" - 2), "if n" > 2):}}`
Write the first 6 terms of the sequences whose nth term an is given below
an = `{{:("n", "if n is" 1"," 2 "or" 3),("a"^("n" - 1) + "a"_("n" - 2) + "a"_("n" - 3), "if n" > 3):}`
Write the nth term of the following sequences.
`1/2, 3/4, 5/6, 7/8, 9/10, ...`
Write the nth term of the following sequences.
6, 10, 4, 12, 2, 14, 0, 16, −2, . . .
Write the nth term of the sequence `3/(1^2 2^2), 5/(2^2 3^2), 7/(3^2 4^2), ...` as a difference of two terms
If tk is the kth term of a G.P., then show that tn – k, tn, tn + k also form a GP for any positive integer k
The AM of two numbers exceeds their GM by 10 and HM by 16. Find the numbers
If the roots of the equation (q – r)x2 + (r – p)x + p – q = 0 are equal, then show that p, q and r are in AP
Choose the correct alternative:
If a, 8, b are in A.P, a, 4, b are in G.P, if a, x, b are in HP then x is
Choose the correct alternative:
The sequence = `1/sqrt(3), 1/(sqrt(3) + sqrt(2)), 1/(sqrt(3) + 2sqrt(2)) ...` form an
Choose the correct alternative:
The nth term of the sequence 1, 2, 4, 7, 11, …… is
Choose the correct alternative:
The nth term of the sequence `1/2, 3/4, 7/8, 15/16, ...` is
