find the smallest number of terms of the geometric progression 2,3,9/2, which must be taken so that the sum exceeds 60

7

Step-by-step explanation:

common ratio: 3/2=1.5

Sum of first nth term: S = a₁ * (1-rⁿ) / (1-r)

60 = 2 * (1 - 1.5ⁿ) / (1 - 1.5)

1.5ⁿ = 16

n = 6.8

s>60    n=7

check: S₇ = 2 * (1-1.5⁷) / (1-1.5) = 64.34

           S₆ = 2 * (1-1.5⁶) / (1-1.5) = 41.56

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

b. hannah is playing with her cousin at