Class 11

Math

Algebra

Sequences and Series

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

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If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the $20_{th}$ term.

Determine the AP whose third term is 16 and the $7_{th}$term exceeds the $5_{th}$term by 12.

A ladder has rungs 25 cm apart, (see Figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are $221 $m apart, what is the length of the wood required for the rungs?

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1 + $32 $+$94 $$+˙˙˙$

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

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

In a school students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?