Question

Orcas (killer whales) kill sharks by torpedoing up into a
shark's stomach from underneath, causing the shark to
explode.​

Answer 1

Explanation:

S=4+11+22+37+56+………………………….+tn-1+tn………………….(1)

S. = 4+11+22 +37+56+……………………………..+tn-1+tn…………(2)

Subtracting eqn (2) from (1)

0=4+7+11+15+19+……………………+.n terms. -tn

tn= 4+[7+11+15+19+…………………..+(n-1)term.]

tn=4+(n-1)/2.[2.7+(n-1-1).4]

tn=4+(n-1)/2.2[7+2n-4]

tn=4+(n-1).(2n+3)

tn=4+2n^2+n-3

tn=2n^2+n+1.

Sn= sigma (2n^2+n+1)

= 2.sigma n^2+sigma n+sigma 1

=2[n(n+1)(2n+1)/6]+n(n+1)/2 + n

=n[(n+1)(2n+1)/3+(n+1)/2+1]

=n/6.[2.(n+1)(2n+1)+3(n+1)+6]

=n/6.[4n^2+6n+2+3n+3+6]

=n.(4n^2+9n+11)/6. Answer