Series

TASK: to find out the number of the m th term of the original series.

Serial No.

If Original Serial no. is given, Corresponding Recast Serial no. can be found out by the following formula:--

* recast serial no. (rs1) = os1+Math.floor(os1/3)

If Recast Serial no. is given(rs2), Corresponding Original Serial no.(os2a) can be found out by the following formula:--

* If recast serial no. is divisible by 4, original serial no. are NON-EXISTENT.

* If recast serial no. is non-divisible by 4, original serial no. is os2a=rs2 - Math.floor(rs2/4) ;

* Suppose in the recast series, 1st no. is a1, the series is in Arithmetic Progression (AP), common difference (cd) is d, then nth number is a1+(n-1)d.

* Value under original serial no. is given by--

a1+d[os1-1+Math.floor(os1/3) where a1 is 1st term , d=common difference

* sum in AP of recast series=sum1=(rs2/2)*[2a1+(rs2-1)d] or sum1=(rs1/2)*[2a1+(rs1-1)d] as the case may be. Here we have taken rs2. If rs2 no. shows non-existent, then take previous / next serial as the case may be.

* sum in AP of original series = sum1 - (diff/2)[(2a1+4d) +(diff-1)2d]; where diff = os1-rs1;

Exa- Take original serial no. as 7, 1st term as 0 and cd=1.