What is the next number 3,6,4,8,6,12,10

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

8 0

The next ten numbers will be 20,18,36,34,68,66,132,130,260,258. Hope this helps.

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A sequence is constructed according to the following rule: its first term is 7, and each next term is one more than the sum of t

Iteru [2.4K]

Answer:

Step-by-step explanation:

According to the described rule, we have

$a_1=7\\ \\a_1^2=7^2=49\Rightarrow a_2=4+9+1=14\\ \\a_2^2=14^2=196\Rightarrow a_3=1+9+6+1=17\\ \\a_3^2=17^2=289\Rightarrow a_4=2+8+9+1=20\\ \\a_4^2=20^2=400\Rightarrow a_5=4+0+0+1=5\\ \\a_5^2=5^2=25\Rightarrow a_6=2+5+1=8\\ \\a_6^2=8^2=64\Rightarrow a_7=6+4+1=11\\ \\a_7^2=11^2=121\Rightarrow a_8=1+2+1+1=5\\ \\\text{and so on...}$

We can see the pattern

$a_5=a_8=a_{11}=a_{14}=...=5\\ \\a_6=a_9=a_{12}=a_{15}=...=8\\ \\a_7=a_{10}=a_{13}=a_{16}=...=11$

In other words, for all $k\ge 2$

$a_{3k-1}=5\\ \\a_{3k}=8\\ \\a_{3k+1}=11$

Now,

$a_{2018}=a_{3\cdot 673-1}=5$

7 0

3 years ago

For a project, Gabrielle made a model of an Egyptian pyramid. The square base has a side length measuring 10 inches. The pyramid

Varvara68 [4.7K]

The pyramid is shown in the diagram below.
The pyramid is built from four congruent triangles and one square as the base

We have the side of the square, so the area is = 10×10 = 100

We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.

Using the Pythagoras rule
Height of triangle = $\sqrt{12^{2}+ 5^{2} } =13$

Area of one triangle = 1/2×10×12=60
Surface area of the pyramid = 100 + (4×60) = 340 square inches

3 0

3 years ago

Read 2 more answers

How to find the rule for the nth term of a geometric sequence with changing common ratio?

ki77a [65]

Hmmm... a geometric sequence MUST have a fixed common ratio. If it is changing, then the sequence you are looking at might not be a geometric sequence at all. We'd need to see an example to be sure.

6 0

3 years ago

Hank’s pickup can travel 60 miles on 5 gallons of gas. How many gallons will Hank’s pickup need to travel 36 miles

Scorpion4ik [409]

60 / 5 = 12 miles per gallon

36 miles = 12 miles / gal * x gallons

divide by 12

36/12 =x gallons

3 =x

He needs 3 gallons

7 0

3 years ago