Home
Class 12
MATHS
If a(1),a(2),a(3),"........" is an arith...

If `a_(1),a_(2),a_(3),"........"` is an arithmetic progression with common difference 1 and `a_(1)+a_(2)+a_(3)+"..."+a_(98)=137`, then find the value of `a_(2)+a_(4)+a_(6)+"..."+a_(98)`.

Text Solution

Verified by Experts

`a_(1)+a_(2)+"....."+a_(98)=137`
`(98)/(2)(a_(1)+a_(98))=137`
`a_(1)+a_(2)+97=(137)/(49),2a_(1)+97=(137)/(49)`
`2a_(1)=(137)/(49)-97,a_(1)=(1)/(2)(137-4753)/(49)`
`a_(1)=-(4616)/(2xx49),a_(1)=(2308)/(49)" " "........(i)"`
`a_(2)+a_(4)+"......+"a_(98)=(a_(1)+1)+(a_(1)+3)+"........"+(a_(1)+97)" "[:.d=1]`
`49a_(1)+(1+3+"......."+97)`
`=-49xx(2308)/(49)+(49)/(2)(1+97)`
`=-2308+49^(2)`
`=-2308+2401=93`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

If a_(1),a_(2),a_(3),...,a_(n) is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan^(-1)(d/(1+a_(1)a_(2)))+tan^(-1)(d/(1+a_(2)a_(3)))+...+tan^(-1)(d/(1+a_(n-1)*a_(n)))]

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent

(1+x-2x^(2))^(6)=1+a_(1),x+a_(2)x^(2)+….+a_(12)^(12) then the value of a_(2) +a_(4)+a_(6)+….+a_(12)=………

If a_(1),a_(2),a_(3),"......" be in harmonic progression with a_(1)=5 and a_(20)=25 . The least positive integer n for which a_(n)lt0 is

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

The sequence a_(1),a_(2),a_(3),".......," is a geometric sequence with common ratio r. The sequence b_(1),b_(2),b_(3),".......," is also a geometric sequence. If b_(1)=1,b_(2)=root4(7)-root4(28)+1,a_(1)=root4(28)" and "sum_(n=1)^(oo)(1)/(a_(n))=sum_(n=1)^(oo)(1)/(b_(n)) , then the value of (1+r^(2)+r^(4)) is

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .