Class 11

Math

Algebra

Sequences and Series

If first three terms of the sequence $1/16,a,b,61 $ are in geometric series and last three terms are in harmonic series, then find the values of $aandb˙$

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

Find the sum to n terms of the series :$1_{2}+(1_{2}+2_{2})+(1_{2}+2_{2}+3_{2})+˙˙˙$

Find the sum of the first 22 terms of the AP : 8,3,-2, . . . .

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:

Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the $4_{th}$by 18.

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Find the $10_{th}$term of the AP : 2, 7, 12, . . .

If $a−bxa+bx =b−cxb+cx =c−dxc+dx (x=0),$then show that a, b, c and d are in G.P.