Question

Find a formula for Sn, (n is greater than or equal to 1) for the sequence 2, 5, 10, 17, 26...

Answer 1

i see the pattern.....3, 5, 7, 9...but ive always been bad at writing the sequence/formula

Answer 2

your pattern is correct.
we should use this pattern in order to find each term in the original sequence.
each term in the original sequence is in fact a sum of this pattern + 2.

Answer 3

the sum of n terms in the pattern is given by :
Pn = (n/2) * (b1 + bn) = (n/2) * (4 + 2n)

follow ?

Answer 4

looks like you are not here so ill just keep on writing and hope youll understand.

so now we have
Pn = n^2 + 2n
which is the sum of n terms in the pattern.
(for example P1 = b1 = 3)

now for the original sequence.
the sum of n terms in the original sequence will be given by:

Answer 5

in the last line i tried to draw the Sum sign

Answer 6

In order to treat the Sum you should know that there is a known expression for the sum of n^2 first terms (and as well for the first n which you can find yourself).

Answer 7

there is a problem with the index of the sum.. sorry
it should be from t=1 to t=n-1 and not t=n

Answer 8

im still confused:( sorry im at work right now so ill check back on my lunch period!

Answer 9

someone please help!! this homework is due tonight and i have no idea what im doing:(