An=a1r^(n-1)

given
a5=1/24
a10=1/768

we know that
a5=1/24=a1r^(5-1) and
a10=1/768=a1r^(10-1)

so
1/24=a1r^4
1/768=a1r^9

(a1r^9)/(a1r^4)=r^5=(1/768)/(1/24)=1/32

r^5=1/32
take 5th root of both sides
r=1/2

we have
a5=a1r^4=1/24
evaluate r^4 or (1/2)^4
1/16
a1(1/16)=1/24
times both sides by 16/1
a1=16/24
a1=2/3

the first term is 2/3

7 0

3 years ago

BD is the angle bisector of

AlexFokin [52]

Note: Let us consider, we need to find the $m\angle ABC$ and $m\angle DBC$ .

Given:

In the given figure, BD is the angle bisector of ABC.

To find:

The $m\angle ABC$ and $m\angle DBC$ .

Solution:

BD is the angle bisector of ABC. So,

$m\angle ABD=m\angle DBC$

$3x=x+20$

$3x-x=20$

$2x=20$

Divide both sides by 2.

$x=\dfrac{20}{2}$

$x=10$

Now,

$m\angle DBC=(x+20)^\circ$

$m\angle DBC=(10+20)^\circ$

$m\angle DBC=30^\circ$

And,

$m\angle ABC=(3x)^\circ+(x+20)^\circ$

$m\angle ABC=(4x+20)^\circ$

$m\angle ABC=(4(10)+20)^\circ$

$m\angle ABC=(40+20)^\circ$

$m\angle ABC=60^\circ$

Therefore, $m\angle DBC=30^\circ,m\angle ABD=30^\circ$ and $m\angle ABC=60^\circ$ .

8 0

2 years ago

What number nearest to 100,000 is exactly divisible by 2, 3, 4, 5, 6 and 7?

navik [9.2K]

First find the numbers with the factors of:
2,3,4,5,6,7
find the minum
if something has a factor of 6 then it also has a factor of 3 and 2 so just multiply by the lcm of all of them which is found by
2=2
3=3
4=2 times 2
5=5
6=2 times 3
7=7

LCM=2 times 2 times 3 times 5 times 7=420

now divide 100000 by 420 and round down
100000/420=238.095=238.1 round doen 238

multiply 420 by 238 and get 99960

that is the answer 99960

4 0

3 years ago