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
nikdorinn [45]
3 years ago
10

If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21

Mathematics
1 answer:
Ilya [14]3 years ago
3 0
This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34  + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}

and now let's use those 2 found folks, to get the 21st term,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104
You might be interested in
3/4•3/4???? I can’t do it in my head and I don’t know how to make a decimal into a fraction
Monica [59]

Answer:

0.5625

Step-by-step explanation:

3/4 as a decimal is 0.75

0.75×0.75=0.5625

4 0
3 years ago
Read 2 more answers
Please help me I honestly have zero clue how to answer this question
Iteru [2.4K]

Step-by-step explanation:

n = 3 \times 5 {}^{2}   \times  {x}^{3}

Square both sides of the equation.

{n}^{2}  = (3 {}^{2}  \times 5 {}^{4}  \times  {x}^{6} )

5 {n}^{2}  = 5(3 {}^{2}  \times  {5}^{4}  \times  {x}^{6} )

6 0
2 years ago
2a+b=15.7 what’s the possible values of b
Fiesta28 [93]

Answer:

b = 15.7 -2a

Step-by-step explanation:

You are asking us to solve for b

2a +b = 15.7

Subtract 2a from each side

2a-2a+b = 15.7 -2a

b = 15.7 -2a

4 0
3 years ago
Please help with these too (10-15)
kakasveta [241]
10. 64in > 5ft
11. 2 mi < 3,333yds
12. 36yd 2 ft< 114 ft 2 in
13. They are =
14. 4ft 7in < 56 in
15. 25 ft > 8yd 11 in
4 0
3 years ago
Read 2 more answers
How many sides does a regular polygon have if the measure of one of it's interior angles is 144?
butalik [34]
Each Interior Angle = 180° - (360 / sides)
144 = 180 - (360 / sides)
(360 / sides) = 36
sides = 360 / 36
sides = 10
It is a decagon.
Source:
http://www.1728.org/polygon.htm


6 0
3 years ago
Other questions:
  • Find sin(x). I need help.
    11·1 answer
  • You buy the same number of brushes,rollers,and paint cans. Write an expression in simplest form that represents the total amount
    10·1 answer
  • GEOMETRY. PLEASE HELP ​
    11·1 answer
  • Which angle is adjacent to _DFE?<br> ZAFB<br> ZAFC<br> OBFD<br> _BFC
    7·1 answer
  • Which set of ordered pairs does not represent a function? { ( − 3 , − 1 ) , ( 8 , − 1 ) , ( 0 , − 5 ) , ( − 9 , − 2 ) } {(−3,−1)
    13·1 answer
  • Find the areas of the trapezoid<br> Due soon! I WILL GIVE BRAINLIEST!! WORTH 46 points (92 total)
    6·2 answers
  • Find the area of the trapezoid
    9·2 answers
  • What would be the next in the sequence if the pattern went 71,70,73,72,75
    8·1 answer
  • What should a bank statement include
    10·1 answer
  • A triangle has an angle that measures 95°. The other two angles are in a ratio of 6:11. What are the measures of those two angle
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!