class 11

Math

Algebra

Sequences and Series

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

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How many two–digit numbers are divisible by 3?

Write first four terms of the AP, when the first term a and the common difference d are given as follows:(i) a = 10, d= 10 (ii) a = –2, d = 0 (iii) a = 4, d = – 3 (iv) a = – 1, d = 1/2(v) a = – 1.25, d = – 0.25

In a factory, 150 workers were engaged to finish a piece of work in a certain number of days. However, if 4 workers are dropped everyday, except the first day, it will take 8 more days to finish the work. Find the number of days in which the work was to be completed.

Show that $a_{1},a_{2},…,a_{n},…$form an AP where $a_{n}$is defined as below : (i) $a_{n}=3+4n$ (ii) $a_{n}=9−5n$. Also find the sum of the first 15 terms in each case.

Find the sum of first $n$ terms of the following series:$5+11+19+29+41+˙$

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 of integers from 1 to 100 that are divisible by 2 or 5.

Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_{n}$the nth term of the AP: