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IrinaK
2 months ago
8

What is a3 in an arithmetic sequence in which a10=41 and a15=61

Mathematics
2 answers:
babunello [11.8K]2 months ago
8 0
The third term needed in the sequence is 13. Step-by-step explanation: We need to determine the third term of an arithmetic sequence where the 10th term is 41 and the 15th term is 61. We know that the nth term of an arithmetic sequence is defined by the formula with first term a and common difference d. Based on the given data, we have two equations. By subtracting the first equation from the second, we derive further insights. From the first equation, we can conclude the necessary value. Therefore, the third term in the sequence equals 13.
zzz [12.3K]2 months ago
8 0
\bf \begin{array}{llll}
term&value\\
-----&-----\\
a_{10}&41\\
a_{11}&41+d\\
a_{12}&(41+d)+d\\
&41+2d\\
a_{13}&(41+2d)+d\\
&41+3d\\
a_{14}&(41+3d)+d\\
&41+4d\\
a_{15}&(41+4d)+d\\
&41+5d=61
\end{array}
\\\\\\
41+5d=61\implies 5d=20\implies d=\cfrac{20}{5}\implies \boxed{d=4}\\\\
-------------------------------\\\\

\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}\\
----------\\
d=4\\
n=10\\
a_{10}=41
\end{cases}
\\\\\\
41=a_1+(10-1)4\implies 41=a_1+36\implies \boxed{5=a_1}

therefore

\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}\\
----------\\
d=4\\
n=3\\
a_{1}=5
\end{cases}
\\\\\\
a_3=a_1+(3-1)4\implies a_3=5+(3-1)4

and you are probably aware of the amount.
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Adam can earn money recycling aluminium cans .each can weighs 15g and he can get paid 50p per kg . If Adam earns £15 , how many
Leona [12618]

There are 0.015 kilograms in 15 grams. Since each can weighs 0.015 kg and the payment rate is 50p per kilogram, 0.015 multiplied by 66 amounts to 1 kilogram! Therefore, 66 cans are needed to generate one kilogram. As a result, earning £15 would mean that with 2 kg equating to one dollar, then 15 multiplied by 2 equals 30. Consequently, 66 times 30 gives 1980!

66 relates to each kilogram, and 30 indicates how many 50p are required for one dollar!

Thus, to obtain £15, Adam has to recycle a total of 1980 cans!


7 0
3 months ago
Greg and Marti are racing remote control cars. The race starts at t=0 and the cars distance is measured from the start line. Bot
PIT_PIT [12445]

Response:

  • Marti is declared the winner

Step-by-step explanation:

Continuation of question:

  • After 10 seconds, the race concluded. The winner is the racer farthest from the starting point. Which car deserves the title of winner? Use mathematical reasoning to support your conclusion.
  • Table is attached

Solution

Greg

  • Travel speed = 13 ft/s
  • Initial position = 30.7 ft from the starting point after 2 seconds
Distance from the starting point after 10 seconds:

30.7 + 13*(10 - 2) = 30.7 + 13*8 = 30.7 + 104 = 134.7 ft
Marti

Travel speed = 16.5 ft/s
  • Starting position = 2 ft from the beginning line
Distance from starting point after 10 seconds:

2 + 10*16.5 = 2 + 165 = 167 ft
  • In comparing the distances from the start line, 134.7 ft against 167 ft, Marti is further from the start line and is thus declared the winner.

8 0
1 month ago
Read 2 more answers
Krystal gets paid $750 every two weeks. She wants to save money for next month's rent but she also needs clothes. Does Krystal h
lawyer [12517]

Answer:

How much is the rent? And how many clothes does she want to buy?

Step-by-step explanation:

6 0
3 months ago
Read 2 more answers
Use this information to find the value of b.<br><br><br>c = 25<br><br>s = 9<br><br><br>b = 4c - s2
PIT_PIT [12445]
Greetings!

Let's rewrite the equation:
b = 4c - s².
Plug in your values:
b = 4(25) - (9)²
Now simplify:
4 times 25 equals 100
9 squared equals 81
So, b = 100 - 81
Calculate:
100 minus 81 equals 19
b is 19.

I hope this helps!
<span>Best of luck:) </span>

<span>- Hannah ❤</span>
3 0
3 months ago
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