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.In President Sergio Osmeña High School, suspension of classes is announced through text brigade. One stormy day, the principal announces the suspension of

classes to two teachers, each of whom sends this message to two other teachers, and so on. Suppose that text messages were sent in five rounds, counting the principal’s text message as the first, how many text messages were sent in all?


The problem is a geometric sequence.

The sequence in the problem:
       1, 2, 4, 8, 16

To find the total text messages sent, solve for the geometric sequence.
       S _{n} =  \frac{a _{1} (1-r ^{n}) }{1-r}
                             where r ≠ 1

       a₁ = first sequence, 1
       r = common ratio, 2
       n = number of terms, 5 (number of rounds)

S_{5} =  \frac{1 (1-2 ^{5}) }{1-2}

S_{5}=  \frac{1(1-32)}{-1}

S _{5}= \frac{1(-31)}{-1}

S _{5} =  \frac{-31}{-1}

S₅ = 31

ANSWER:  A total of 31 text messages were sent.

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