Describe an infinite geometric series with the beginning value of 2 that converges to 10 what are the first four terms of the series

Step-by-step explanation:

The sum of an infinite geometric series is ...

  S = a1/(1 -r)

where r is the common ratio. The sum will only exist if |r| < 1.

The problem statement tells us S = 10 and a1 = 2, so we have ...

  10 = 2/(1 -r)

  r = 1 -2/10 = 4/5

So the n-th term of the series is ...

  an = a1·r^(n-1)

  an = 2·(4/5)^(n-1)

For values of n = 1 to 4, the terms are ...

  2, 8/5, 32/25, 128/125

moderators are

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.