Directions: Describe the following scientists below and tell something about their contribution on the invention of the microscope. Write your answer on your activity notebook. SCIENTISTS CONTRIBUTIONS 1. Robert Hooke 2. Hans & Zacharias Janssen 3. Anton van Leeuwenhoek 4. Richard Zsigmondy

A Dutch father-son team named Hans and Zacharias Janssen invented the first so-called compound microscope in the late 16th century when they discovered that, if they put a lens at the top and bottom of a tube and looked through it, objects on the other end became magnified.

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for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for