For a given geometric sequence, the 9th term, a9, is equal to 43/256 and the 14th term, a14, is equal to 172. Find the value of the 18 term

Step-by-step explanation:

From the question we are told that:

9th term

14th term

Generally the equation for Geometric sequence is mathematically given by

For 9th term

For 14th term

Substitute in 9th term

Therefore First term a is given as

Generally the equation for the 18th term is mathematically given by

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b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b