31+33+35+37+39+41=216=6 step by step explationMATHSIf a sequence or series is not directly in A.P or G.P, then their general terms (l N ) cannot be determined easily. For such cases to determine t n we use the FOLLOWING steps.Step 1: First of all we find the successive DIFFERENCE (first difference, second difference, third difference … so on).Step 2: If first successive difference is in A.P, then general term can be taken as t n =an 2 +bn+c (i.e. consider t n as quadratic polynomial in the decreasing power of n with constants a,b,c ).Step 3: If the second, third successive differences are in A.P, then t n =an 3 +bn 2 +cd+d for second successive difference in A.P and so on where a,b,c,d are constants whose order can be changed.Step 4: If the first difference in step 1 is in G.P, then take t n =ar n−1 +bn+c. Similarly if second, third difference are in G .P, then general terms are considered by t n =ar n−1 +bn 2 +cn+d and t n =ar n−1 +bn 3 +cn 2 +dn+e respectively where a,b,c,d,e… are constants whose orders can be changed.Now consider the sequencesP:9,16,29,54,103,…Q:4,14,30,52,80,114,…R:2,12,36,80,150,252,…S:2,5,12,31,86,…On the basis of above DATA (information) answer the following questions:The sum of n terms ofthe sequences P & S are respectively