Advertisements
Advertisements
Question
Write the nth term of the following sequences.
2, 2, 4, 4, 6, 6, . . .
Solution
The odd terms are a1 = 2, a3 = 4, a5 = 6
The even terms are a2 = 2, a4 = 4, a6 = 6
∴ an = `{{:("n" + 1, "if n is odd"),("n", "if n is even"):}`
APPEARS IN
RELATED QUESTIONS
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
`(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 = `{{:("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 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, ...`
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
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
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 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
