Find the sequence of the first five partial sums

S1, S2, S3, S4, and S5 of the geometric sequence by adding terms.
9, 12, 16, 64/3, 256/9,...

S1 =
S2 =
S3 =
S4 =
S5 =

Ayo Steve don't be rude

S5

S10

S1 = 9

S2 = 9 + 12 = 21
S3 = 9 + 12 + 16 = 37
S4 = 9 + 12 + 16 + 64/3 = 135/3 + 4/3 = 139/3
S5 = 9 + 12 + 16 + 64/3 + 256/9 = 405/9 + 288/9 + 256/9 = 949/9

So the sequence of the first five partial sums is:
S1 = 9
S2 = 21
S3 = 37
S4 = 139/3
S5 = 949/9

To find the sequence of the first five partial sums (S1, S2, S3, S4, and S5) of the given geometric sequence, we need to find the sum of the first few terms.

A geometric sequence follows the pattern where each term is multiplied by a common ratio to get the next term. In this case, we can see that the common ratio is 4/3.

Now, let's calculate the partial sums step by step:

S1 = the first term = 9

S2 = S1 + the second term = 9 + 12 = 21

S3 = S2 + the third term = 21 + 16 = 37

S4 = S3 + the fourth term = 37 + (64/3) = 181/3

S5 = S4 + the fifth term = (181/3) + (256/9) = (543 + 256) / 9 = 799/9

Therefore, the sequence of the first five partial sums is:

S1 = 9
S2 = 21
S3 = 37
S4 = 181/3
S5 = 799/9

come on -- just add them up.

S1 = 9
S2 = 9+12 = 21
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