class 11

Math

Algebra

Sequences and Series

If $(10)_{9}+2(11)_{1}(10)_{8}+3(11)_{2}(10)_{7}+¨+10(11)_{9}=k(10)_{9}$, then k is equal to

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Write the first five terms of the sequence whose $n_{th}$terms are : $a_{n}=n(n+2)$

Find the indicated terms of the sequence whose $n_{th}$terms are : $a_{n}=n+3n(n−2) $; $a_{20}$

For the following AP's, write the first term and the common difference:(i) $3,1,−1,−3,…$(ii) $−5,−1,3,7,…$(iii) $31 ,35 ,39 ,311 ……$(iv) $0.6,1.7,2.8,3.9,…$

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $π=722 $)

The $5_{th}$, $8_{th}$and $11_{th}$terms of a G.P. are p, q and s, respectively. Show that $q_{2}=ps$.

Write the first five terms of the sequence whose $n_{th}$terms are : $a_{n}=n+1n $

If the $4_{th}$, $10_{th}$and $16_{th}$terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Find the sum of odd integers from 1 to 2001.