What is a common ratio of the geometric sequence whose first term
is 5 and third term is 245?
(1) 7 (3) 120
(2) 49 (4) 240

the common ratio of the geometric sequence is 7

Step-by-step explanation:

In a geometric sequence, consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 5

For the third term,

n = 3

Therefore,

245 = 5 × r^(3 - 1)

245/5 = r^²

49 = r²

Taking square root of both sides of the equation, it becomes

r = 7

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm