Question

The height of sunflowers can be represented by a geometric sequence. The first measurement showed the sunflowers to be 12 inches tall, while the 5th measurement showed the sunflowers to be 20.27 inches tall. Represent this function using sequence notation.
PLEASEEEEE HELPP!!!!!!!!!! and answer STEP BY STEP!!!!

Answer 1

The first term is 12.

The second term is 12r, where r is the common ratio. We multiply any term by the common ratio to get the next term.

The third term is (12r)*r = 12r^2.

The fourth term is (12r^2)*r = 12r^3

The fifth term is (12r^3)*r = 12r^4. The fifth term is also 20.27 which was given to us.

Equate the two items and solve for r.

12r^4 = 20.27

r^4 = 20.27/12

r = (20.27/12)^(1/4)

r = 1.14003484493186 which is approximate

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We can now find the approximate terms of this sequence

a = first term

a = 12

b = second term

b = a*r

b = 12*1.14003484493186

b = 13.6804181391823

c = third term

c = b*r

c = 13.6804181391823*1.14003484493186

c = 15.5961533719058

d = fourth term

d = c*r

d = 15.5961533719058*1.14003484493186

d = 17.7801582908741

e = fifth term

e = 17.7801582908741*1.14003484493186

e = 20.2700000000006

The 6 at the end is due to rounding error.

Therefore, the sequence has these five terms in the exact order shown

• 12
• 13.6804181391823
• 15.5961533719058
• 17.7801582908741
• 20.27

The sequence notation of this function is

{12, 13.6804181391823, 15.5961533719058, 17.7801582908741, 20.27}

Round those values however you need to.