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masya89 [10]
3 years ago
14

A recursive rule for an arithmetic sequence is a1=4;an=an−1−3 . What is the explicit rule for this sequence? Enter your answer i

n the box. an=
Mathematics
1 answer:
Westkost [7]3 years ago
5 0

Answer:

The explicit rule for the arithmetic sequence is given by:

a_n = a_1+(n-1)d       ......[1]

where,

a_1 is the first term

n is the number of terms and

d is the common difference for two consecutive terms.

As per the statement:

A recursive rule for an arithmetic sequence is:

a_1 = 4

a_n = a_{n-1}-3

The recursive formula for the arithmetic sequence is given by:

a_n = a_{n-1}+d

then;

On comparing we get;

d = -3

Substitute the given values in [1] we have;

a_n = 4+(n-1)(-3)

⇒a_n = 4 -3n+3 = 7-3n

Therefore, the explicit rule for this sequence is, a_n = 7 -3n

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How to solve this problem​
nevsk [136]

Let C be the center of the circle. The measure of arc VSU is 2+114x, so the measure of the minor arc VU is 360-(2+114x)=358-114x. The central angle VCU also has measure 358-114x.

Triangle CUV is isosceles, so the angles CVU and CUV are congruent. The interior angles of any triangle are supplementary (they add to 180 degrees) so

m\angle VCU+2m\angle CUV=180

\implies m\angle CUV=\dfrac{180-(358-114x)}2=57x-89

UT is tangent to the circle, so CU is perpendicular to UT. Angles CUV and VUT are complementary, so

(57x-89)+(31x+3)=90

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\implies x=2

So finally,

m\widehat{VSU}=2+114\cdot2=230

degrees.

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