Class 11

Math

Algebra

Sequences and Series

If the mean of $x,x+2,x+4,x+8$ is $20$ find $x$.

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Find the sum of first 24 terms of the list of numbers whose nth term is given by $a_{n}=3+2n$

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

Find the sum of the following APs : (i) 2, 7, 12, . . . , to 10 terms.

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

Find the $11_{th}$from the last term (towards the first term) of the AP : $10,7,4,˙˙˙,62.$

If a, b, c are in A.P., b, c, d are in G.P. and $c1 ,d1 ,e1 $are in A.P. prove that a, c, e are in G.P.

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

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: