Let ${a_1},{a_2},.....{a_{30}}$ be an AP, $S = \sum\limits_{i = 1}^{30} {{a_i}} $ and $T = \sum\limits_{i = 1}^{15} {{a_{(2i - 1)}}} $ If ${a_5} = 27{\rm{ \,and}}\,\,{\rm{ }}S - 2T = 75,{\rm{then}}\,{\rm{ }}\,\,{a_{10}}$ is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

Let

{a_1},{a_2},.....{a_{30}}

be an AP,

S = \sum\limits_{i = 1}^{30} {{a_i}}

and

T = \sum\limits_{i = 1}^{15} {{a_{(2i - 1)}}}

{a_5} = 27\mathrm{ \,and}\,\,\mathrm{ }S - 2T = 75,\mathrm{then}\,\mathrm{ }\,\,{a_{10}}

is equal to

View answer and explanation

Correct option: C

Option C (52) is correct because by using the properties of arithmetic progressions and the given conditions, we can find the common difference and then calculate a_10.

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Given the sets

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

(ii)

A-(B \cap C)

(iii)

(B \cup C)-A

a,b,c

are in A.P.;

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

are in Suppose

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

, as

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

where

y=x-2

, then

\sum\limits_{{i=0}}^{2012} a_i

equals If

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

and

\log \left(\frac{a}{3 b}\right)

are in

A P

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a, b

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G P

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a, b, c

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\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is