Which of the following is true regarding the image shown.

[rosypetals]

 

[tkhunny]

a21 = 18
a20 = 18 + 2 = 20
a19 = ??

Off you go...

 

[Dr.Peterson]

Which of the following is true regarding the image shown.
View attachment 24052

If you prefer, you can write an equation for [MATH]a_{21}[/MATH] in terms of [MATH]a_1[/MATH] and [MATH]d[/MATH], and then solve for [MATH]a_1[/MATH].

 

[Steven G]

a_1 = a_1
a_2 = a_1 - 1*2 = a-2
a_3 = a_1 - 2*2 = a-4
a_4 = a_1 - 3*2 = a-6
...
a_21 = a_1 - ?*2 = 18.

So solve for a_1 - ?*2 = 18 for a_1, but 1st decide on what ? equals.

 

[Otis]

Here's another way to consider, for students who have a good understanding of arithmetic sequences.

The given information tells us that we get 18, after subtracting twenty 2s from the number a₁.

So, how much did we subtract from a₁ altogether? In other words:

a₁ - (total amount subtracted) = 18

(That's basically what the formula for the nth term is doing.)

?

 

[Deleted member 4993]

View attachment 24052

This is a problem of arithmetic progression.

If the first number is a₁ and the common difference is d, then:

a_n = a₁ + d * (n-1) ................................................(1)

for this problem: a₂₁ = 18 and d = -2

Now use equation (1) - given above - to calculate the numerical value of a₁

 

[Steven G]

Here's another way to consider, for students who have a good understanding of arithmetic sequences.

The given information tells us that we get 18, after subtracting twenty-one 2s from the number a₁.

So, how much did we subtract from a₁ altogether? In other words:

a₁ - (total amount subtracted) = 18

?

...after subtracting twenty-one 2s?

 

[pka]

We see that \(a_n=a_1+d*(n-1)\). That is rather straightforward.
In this problem we are told that \(a_{21}=18~\&~d=-2\) and then ask to find \(a_1\)
Well then: \(18=a_{21}=a_1+(-2)*(21-1)\). Lets ask the student to solve for \(a_1\).

 

[Otis]

… subtracting twenty-one 2s?

Thanks for catching my careless typo. (My hands need a better understanding of APs, ha.)

?