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Maurinko [17]
2 years ago
14

The first term of an arithmetic sequence is 14. The 25th term is 206. What is the common difference of the arithmetic sequence?

Mathematics
2 answers:
larisa [96]2 years ago
3 0

an = a1+ d(n-1)

a1 =14

an=206  when n=25

206 = 14 + d (25-1)

206 = 14 + d * 24

subtract 14 from each side

192 = 24d

divide by 24 on each side

d=8

The common difference is 8

REY [17]2 years ago
3 0

an atirmetic sequence  can be written in form

a_n=a_1+d(n-1)

where a_n is the nth term

a_1 is the first term

d is the common difference

n is the counter variable


so, given that first term is 14 (a_1=14) and given taht 25th term is 206 (a_{25}=206), we want to find d


a_{25}=206

a_{25}=a_1+d(25-1)

206=14+24d

minus 14 both sides

192=24d

divide both sides by 24

8=d

the common difference is 8

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The number 3456 is divisible by wich single-digit number?
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I'm assuming what you mean is what can you divide 3456 by to get a natural number.

First of all every number is divisible by 1.  

Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2.  That would equal 1728.

2456 can also be divided by 3, to get 1782.  

You can also divide it by 4, to get 865.

Divided by 6, it's 576.

Divided by 8, it's 432.

And lastly, 3456 divided by 9 is 384.

So, there isn't just one single-digit number you can divide 3456 by to get a natural number.  You can divide it by 1,2,3,4,6,8, and 9.

Hope that helps!

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juin [17]

Answer:

15°

brainlest

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°.  Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.

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