Find a formula for geometric series that begins with 28, 98, 343,...

Mathematics

1 answer:

otez555 [7]2 years ago

6 0

Answer:

Step-by-step explanation:

In a geometric series, the successive terms differ by a common ratio which is determined by dividing a term by the preceding term.

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 between successive terms in the sequence.

n represents the number of terms in the sequence.

From the seies shown,

a = 28

r = 98/28 = 343/98 = 3.5

The formula representing the nth term of the given sequence would be expressed as

Tn = 28 × (3.5)^(n - 1)

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snow_lady [41]

Answer:

a. FG ≈ 6.983 cm

b. FH = 13.16 cm

Step-by-step explanation:

Corresponding sides of similar triangles are proportional. This means ...

FG/GH = CD/DE

FG = GH(CD/DE) = (9.4 cm)(2.6/3.5) . . . . . . multiply by GH; fill in values

FG ≈ 6.983 cm

And ...

FH/GH = CE/DE

FH = GH(CE/DE) = (9.4 cm)(4.9/3.5)

FH = 13.16 cm

<em>Additional comment</em>

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