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2 years ago

What are the similarities and differences between linear equations and arithmetic sequences?

1 answer:

4 0

Similarities:
Have a consistent change for every interval can be represented as functions of a variable points lie on a line.

Differences: linear equations represent all solutions to all x values, whereas arithmetic sequences pick integer spacing

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Find an equation for the nth term of the arithmetic sequence.

amm1812

Answer:

$a_n=-301 +37(n-1)$

Step-by-step explanation:

arithmetic sequence formula: $a_n=a +(n-1)d$

where $a$ is the first term and $d$ is the common difference

Given:

$a_{10}=32$

⇒ $a +(10-1)d=32$

⇒ $a+9d=32$

Given:

$a_{12}=106$

⇒ $a +(12-1)d=106$

⇒ $a+11d=106$

Rearrange the first equation to make $a$ the subject:

a = 32 - 9d

Now substitute into the second equation and solve for $d$

(32 - 9d) + 11d = 106

⇒ 32 + 2d = 106

⇒ 2d = 106 - 32 = 74

⇒ d = 74 ÷ 2 = 37

Substitute found value of $d$ into the first equation and solve for $a$ :

a + (9 x 37) = 32

a + 333 = 32

a = 32 - 333 = -301

Therefore, the equation is: $a_n=-301 +37(n-1)$

4 0

1 year ago

Help me and am I doing this right

Nat2105 [25]

Looks write but i think ur missing somthing

5 0

2 years ago

House prices in a certain area went

Scorpion4ik [409]

Answer:

£60000

Step-by-step explanation:

8 0

2 years ago

What is the length of chord An in Oo below?

Anika [276]

Answer:

12 units

Step-by-step explanation:

$In\: \odot O,$

chords $\overline{ML}$ and $\overline{AN}$ are equidistant (7.2 units) from the center of the circle O.
Measures of the chords equidistant from the center of the circle are equal.
$\therefore m(chord\:\overline{AN}) =m(chord\:\overline{ML})$
$\because m(chord\:\overline{ML}) = 12\: units$
$\therefore m(chord\:\overline{AN}) = 12\: units$