how can we express 12 cube as sum of consecutive odd no.
Answers
Answer:
31+33+35+37+39+41
=216
=6
step by step explation
MATHS
If 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 sequences
P: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