HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Write the first 6 terms of the sequences whose n^th 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 n^th 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 n^th 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 n^th term a_n is given below

a_n = `{{:("n" + 1,  "if"  "n is odd"),("n",  "if"  "n is even"):}`

Write the first 6 terms of the sequences whose n^th term a_n is given below

a_n = `{{:(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 n^th term a_n is given below

a_n = `{{:("n",  "if n is"  1","  2  "or"  3),("a"^("n" - 1) + "a"_("n" - 2) + "a"_("n" - 3), "if n" > 3):}`

Write the n^th term of the following sequences.
2, 2, 4, 4, 6, 6, . . .

Write the n^th term of the following sequences.
`1/2, 2/3, 3/4, 4/5, 5/6, ...`

Write the n^th term of the following sequences.
`1/2, 3/4, 5/6, 7/8, 9/10, ...`

Write the n^th 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

Write the n^th 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 t_k is the k^th term of a G.P., then show that t_{n – k}, t_n, t_{n + 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 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 p^th, q^th and r^th 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