(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Find the seventh term from the end of the series :

`sqrt(2), 2, 2sqrt(2), ........., 32.`

Find the third term from the end of the G.P.

`2/27, 2/9, 2/3, .........,162.`

For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.

If for a G.P., p^th, q^th and r^th terms are a, b and c respectively; prove that : (q – r) log a + (r – p) log b + (p – q) log c = 0

Q 5

Q 6

Q 7

Q 8

If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.

Q 1.2

Q 2

If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.

Show that : x², b², y² are in A.P.

If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `1/x + 1/y = 2/b`

If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`

Q 6

If a, b and c are in A.P. and also in G.P., show that : a = b = c.

Find the sum of G.P. :

1 + 3 + 9 + 27 + .......... to 12 terms. 

Find the sum of G.P. :

0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.

Find the sum of G.P. :

`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.