1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
laila [671]
3 years ago
13

the first term of an arithmetic sequence is 2 and the sum of the first 15 terms is 292.5. Find the common difference

Mathematics
1 answer:
adelina 88 [10]3 years ago
8 0

Given:

First term of an arithmetic sequence is 2.

Sum of first 15 terms = 292.5

To find:

The common difference.

Solution:

We have,

First term: a=2

Sum of first 15 terms: S_{15}=292.5

The formula of sum of first n terms of an AP is

S_n=\dfrac{n}{2}[2a+(n-1)d]

Where, a is first term and d is common difference.

Putting S_{15}=292.5, n=15 and a=2 in the above formula, we get

292.5=\dfrac{15}{2}[2(2)+(15-1)d]

292.5=\dfrac{15}{2}[4+14d]

292.5=15[2+7d]

Divide both sides by 15.

\dfrac{292.5}{15}=2+7d

19.5=2+7d

19.5-2=7d

17.5=7d

Dividing both sides by 7, we get

\dfrac{17.5}{7}=d

2.5=d

Therefore, the common difference is 2.5.

You might be interested in
ANSWER FAST PLEASE!!!
boyakko [2]
Log₂(6x) - log₂(√x) = 2

log₂[6x/√x] = 2, let's rewrite it in terms of exponent:

(remember : ㏒₂(x) = a  (in exponential form) → x = 2ᵃ

6x/√x = 2²

6x/√x = 4, square both sides:
36x²/x = 16 .Simplify:

36x = 16 and x = 16/36 . So x = 4/9
7 0
3 years ago
What is the equation of the axis of symmetry for the parabola​
ozzi

Answer:

x=3

Step-by-step explanation:

axis of symmetry always pass through X coordinate of vertex.

here vertex is (h,k)= (3,5)

so x coordinate is 3.

so the equation of the axis of the symmetry is X=3

6 0
2 years ago
Read 2 more answers
What is formed when two complementary angles share one ray?
aleksklad [387]

Answer:

B.

the complementary angles form a right angle with the shared ray

5 0
3 years ago
#1 please! will give great rating! please explain to!
ddd [48]
Find the perimiter now

that is right triangle so
when hpotonouse is c and hthe lgs are a and b
a²+b²=c²

given
leg is 8
hypotonuse is 13

8²+b²=13²
64+b²=169
minus 64 from both sides
b²=105
sqrt both sides
b=√105

find total perimiter
8+13+√105=21+√105

times 1/32 for scale
0.65625+0.32021721143623744947565745876628=
0.97646721143623744947565745876628 m=
97.646721143623744947565745876628 cm

A is the answer
7 0
3 years ago
Read 2 more answers
Please help!<br><br> 7.5 in = ________ cm
Naya [18.7K]
The answer is 18 cm because 2.4 cm is in 1 inch. you must multiply 7.5 by 2.4 and get 18
3 0
3 years ago
Read 2 more answers
Other questions:
  • The Science Club can spend at most $400 on a field trip to a dinosaur exhibit. It has enough chaperones to allow at most 100 stu
    13·1 answer
  • Which table shows exponential decay?
    11·1 answer
  • Kevin wants to buy a video game for $45. He also wants to buy 2 game
    13·1 answer
  • A show is on Friday, Saturday and Sunday
    13·1 answer
  • PLEASE HELP !!!
    14·1 answer
  • Which pair of triangles are cungruent
    6·1 answer
  • At a school costume party, seven girls wore masks nine
    12·1 answer
  • The elves at Santa’s Workshop are trying to wrap the biggest box they can with the last bit of wrapping paper they have. All of
    12·1 answer
  • Find the magnitude and direction of r+u<br><br> please help !!
    15·1 answer
  • Decimal divison need answer no pdf
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!