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
`(2"n" + 3)/(3"n" + 4)`
उत्तर
an = `(2"n" + 3)/(3"n" + 4)`
a1 = `(2 xx 1 + 3)/(3 xx 1 + 4) = (2 + 3)/(3 + 4) = 5/7`
a2 = `(2 xx 2 + 3)/(3 xx 2 + 4) = (4 + 3)/(6 + 4) = 7/10`
a3 = `(2 xx 3 + 3)/(3 xx 3 + 4) = (6 + 3)/(9 + 4) = 9/13`
a4 = `(2 xx 4 + 3)/(3 xx 4 + 4) = (8 + 3)/(12 + 4) = 11/16`
a5 = `(2 xx 5 + 3)/(3 xx 5 + 4) = (10 + 3)/(15 + 4) = 13/19`
a6 = `(2 xx 6 + 3)/(3 xx 6 + 4) = (12 + 3)/(18 + 4) = 15/22`
∴ The given dequence is `5/7, 7/10, 9/13, 11/6, 13/19, 15/22`, .........
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
`(("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
`(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, . . .
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, . . .
The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP
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 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
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 HM of two positive numbers whose AM and GM are 16, 8 respectively is
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
