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
`(3"n" - 2)/(3^("n" - 1))`
उत्तर
The given nth term is an = `(3"n" - 2)/(3^("n" - 1))`
a1 = `(3 xx 1 - 2)/(3^(1 - 1)) = (3 - 2)/3^0 = 1/1` = 1
a2 = `(3 xx 2 - 2)/(3^(2 - 1)) = (6 - 2)/3^1 = 4/3`
a3 = `(3 xx 3 - 2)/(3^(3 - 1)) = (9 - 2)/3^2 = 7/9`
a4 = `(3 xx 4 - 2)/(3^(4 - 1)) = (12 - 2)/3^3 = 10/27`
a5 = `(3 xx 5 - 2)/(3^(5 -1)) = (15 - 2)/3^4 = 13/81`
a6 = `(3 xx 6 - 2)/(3^(6 -1)) = (18 - 2)/3^5 = 16/243`
∴ The given sequence is `1, 4/3, 7/9, 10/27, 13/81, 16/243`
`1/1 (1/3)^0, 4(1/3)^1, 7(1/3)^2, 10(1/3)^3, 13(1/3)^4, 16(1/3)^5`
1, 4, 7, 10, 3, 16, ........... is in A.P.
`(1/3)0, 1/3, (1/3)^2, 1/3)^3, (1/3)^4, (1/3)^5` ........... is in G.P.
∴ The given sequence is A.G.P.
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
`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
`(2"n" + 3)/(3"n" + 4)`
Write the first 6 terms of the sequences whose nth term an is given below
an = `{{:("n" + 1, "if" "n is odd"),("n", "if" "n is even"):}`
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, 2/3, 3/4, 4/5, 5/6, ...`
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
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:
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
