4) Find 1 X 5+ 3 * 7 + 5 x 9 + 7 x 11
... upto n terms
Answers
Answered by
14
Step-by-step explanation:
the given sequence is obtained by multiplying two A.Ps..
A.P 1.. 1+3+7....
A.P 2.. 5+7+9....
we know Sn=summation of tn
tn of above sequence is:-
(tn of A.P1) (tn of A.P2)
=>(1+(n-1)2) (5+(n-1)2)
=>(2n-1) (2n+3)
=>4n²-3+4n
so, summation of 4n² -3 +4 n
is:
=>4n(n+1)(2n+1)/6 - 3n +4n(n+1)/2
[as n²=n(n+1)(2n+1)/6 and
n=n(n+1)/2]
=>{4n(n+1)(2n+1) -18n+12n(n+1)}/6
=>{4n(n+1)(2n+1+3)-18n}/6
=>{4n(n+1)(2n+4)-18n)/6
=>(4n(n+1)(n+2)-9n)/3
Similar questions