Series

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

 Original Serial No. Numbers

 Recast  Serial No. 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.

 Original  Serial No(os1) .- Given First term of the Series (a1) (you can change the value) Common Difference (d) (you can change the value) Find out --> Recast  Serial No.(rs1) Value  under the Given Original serial no.(an) Sum of recast series up to rs1/rs2 (sum1) Sum of original series up to os1/os2 (sum2) Recast Serial no.- Given (rs2) Value under the recast serial no.(vr1) Original Serial No.(os2) Value under the Original serial no.(vr2)