Write the explicit formula for the arithmetic sequence 11, 14, 17, 20, . . . What is term number 54 in this sequence?

see explanation

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 11 and d = a₂ - a₁ = 14 - 11 = 3, then

= 11 + 3(n - 1) = 11 + 3n - 3 = 3n + 8

Thus

a₅₄ = 3(54) + 8 = 162 + 8 = 170

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c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.