Advertisements
Advertisements
प्रश्न
Write the nth term of the following sequences.
`1/2, 3/4, 5/6, 7/8, 9/10, ...`
Advertisements
उत्तर
The given sequence is `1/2, 3/4, 5/6, 7/8, 9/10, ...`
The terms in the numerator are 1, 3, 5, 7, 9, …
a = 1 , d = 3 – 1 = 2
an = a + (n – 1) d
an = 1 + (n – 1)2
an = 1 + 2n – 2 = 2n – 1
The terms in the denominator are 2, 4, 6, 8, 10, …
a = 2, d = 4 – 2 = 2
an = a + (n – 1) d
an = 2 + (n – 1)(2)
an = 2 + 2n – 2 = 2n
∴ The nth term of the given sequence is an = `(2"n" - 1)/(2"n")` for all n ∈ N
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
`1/(2^("n"+ 1))`
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))`
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
2018
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 nth term of the following sequences.
2, 2, 4, 4, 6, 6, . . .
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
If a, b, c are in geometric progression, and if `"a"^(1/x) = "b"^(1/y) = "C"^(1/z)`, then prove that x, y, z are in arithmetic progression
The AM of two numbers exceeds their GM by 10 and HM by 16. Find the numbers
If a , b , c are respectively the pth, qth and rth terms of a G . P show that (q – r) log a + (r – p) log b + (p – q) log c = 0
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
