Arare bacterial culture is being grown in a lab. as time passes, the cells multiply in a specific pattern. after 1 day, there is only 1 cell. after 2 days, there are 9 cells. after 3 days, there are 20 cells. after 4 days, there are 34 cells. how many cells will there be after seven days? a.149b.120c. 98d.94

the equation is, 
a_n = a_(n–1) + 3 * n + 2

Substituting the values for day 4, 

20 + 3*4 + 2 = 34

Thus the equation is correct

Therefore to calculate for a_n at n = 7 or a_7, we must calculate a_5 and a_6 first.

a_5 = 34 + 3*5 + 2 = 51

a_6 = 51 + 3*6 + 2 = 71

Hence,

a_7 = 71 + 3*7 + 2 = 94

D. 94

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