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Trava [24]
3 years ago
9

Write the first five terms of the geometric sequence in which a1=64 and the common ratio is 5/4

Mathematics
1 answer:
natita [175]3 years ago
8 0

Remember that finding terms in a geometric sequence is done by multiplying the previous term by a common ratio r. For example, we can say:

a_2 = a_1 r

a_3 = a_2 r = (a_1 r)r = a_1 r^2


We have a_1 = 64. To find a_2, let's multiply this term by \frac{5}{4}:

a_2 = 64 \cdot \frac{5}{4} = 80


Now, let's use this to find all of our other terms:

a_3 = 80 \cdot \frac{5}{4} = 100

a_4 = 100 \cdot \frac{5}{4} = 125

a_5 = 125 \cdot \frac{5}{4} = \frac{625}{4}


Thus, our terms are 64, 80, 100, 125, and (625/4).

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