Class 11

Math

Algebra

Sequences and Series

If $4AM_{′}s$ are inserted between $1/2$ and $3$ then $3_{rd}$ AM is

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The sum of some terms of G. P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

The sums of n terms of two arithmetic progressions are in the ratio $5n+4:9n+6$. Find the ratio of their $18_{th}$terms.

Find the sum to infinity of the following Geometric Progression:$4−3 ,163 ,64−3 ,…$

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find :(i) the production in the 1st year(ii) the production in the 10th year(iii) the total production in first 7 years

If A.M. and GM. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

Write the first five terms of the sequence and obtain the corresponding series : $a_{1}=3,a_{n}=3a_{n−1}+2$for all $n>1$

Find the $10_{th}$and $n_{th}$terms of the G.P. 5, 25, 125, . . .

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?