Class 11

Math

Algebra

Sequences and Series

A.M. of $1,2,x,3$ is $0$, then $x=$ _____.

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

If a, b, c and d are in G.P. show that $(a_{2}+b_{2}+c_{2})(b_{2}+c_{2}+d_{2})=(ab+bc+cd)_{2}$.

Find the sums given below : (i) $7+1021 +14+…+84$(ii) $34+32+30+…+10$(iii) $5+(8)+(−11)+…+(230)$

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

A fanner buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

If the sum of the first n terms of an AP is $4n−n_{2}$, what is the first term (that is $S_{1}$)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?(i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.(ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre of digging, when it costs Rs.150 for the first metre and rises by Rs. 50 for each subsequent metre. (iv) The amount of money in the account every year, when \displaystyle{10000}{i}{s}{d}{e}{p}{o}{s}{i}{t}{e}{d}{a}{t}{c}{o}{m}{p}{o}{u}{n}{d}\int{e}{r}{e}{s}{t}{a}{t}{8}\%{p}{e}{r}{a}\cap{u}{m}.

Find the sum to n terms of the series :$1×2+2×3+3×4+4×5+......$