Note: the term is written as a1, the 1 is small which is below the a.
The first four terms in a sequence, and the rules that define them, are shown below.
a1 = 4
a2 = 2a1 + 3
a3 = 2a2 + 3
a4 = 2a3 + 3
What is the value of a4, the fourth term shown in the sequence above?
A. 25
B. 35
C. 41
D. 53
what does the meaning of the symbol a1?
2007-12-26 12:11:15 · 18 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Ok a1 in this sense would mean "a sub 1".
It's just a way of stating the terms in a sequence. Sequences are nothing but patterns of numbers. You should see the pattern as we go along.
Now in order to find a4 we need to plug in the information we already have.
Looks like we are given a1=4.
Ok so let's plug a1 into the a2 equation to see what we get,
a2= 2(4) +3
a2 =8 + 3
a2 = 11.
Ok! we now have a1 and a2. Now let's find a3.
a3 = 2(11) +3
a3 =22 + 3
a3 = 25.
Now we have a1, a2, and a3. Let's find what we need, a4.
a4 = 2(25) +3
a4 = 50 + 3
a4 = 53
so out of the four options listed, your answer would be D, 53.
2007-12-26 12:24:12 · answer #1 · answered by Chris 3 · 0⤊ 0⤋
We have an arithmetic sequence.
They give you a1, which is read "a sub one."
Got it?
They also give you a list of arithmetic sequences:
a1 = 4
a2 = 2a1 + 3
a3 = 2a2 + 3
a4 = 2a3 + 3
You know that a1 = 4, right?
We plug this value into the second sequence and simplify.
a2 = 2a1 + 3
a2 = 2(4) + 3
a2 = 8 + 3
a2 = 11
We now know that a1 = 4 and a2 = 11.
We plug the value for a2 into the third sequence and simplify.
a3 = 2(11) + 3
a3 = 22 + 3
a3 = 25
We now know a1 = 4, a2 = 11 and a3 = 25
Is this clear so far?
Now that we know a3, we plug that into sequence 4 and simplify to find a4.
a4 = 2a3 + 3
a4 = 2(25) + 3
a4 = 50 + 3
a4 = 53
Final answer: Choice (D) 53
2007-12-26 12:32:40 · answer #2 · answered by Mathland 2 · 0⤊ 0⤋
What is to understand? WOrk it out!
a2=2(a1)+3 = 2(4) +3 = 8+3 =11
a3=2(a2)+3=2(11) +3 = 22 +3 =25
a4 = 2(a3)=3 =2(25) +3 = 50+3 =53
Your answer is D. 53
the symbol a1 (where the 1 is small which is below the a) is called a subscript. It is the first a in a series of a terms that are somehow related to each other, in this case built upon each other.
2007-12-26 12:21:08 · answer #3 · answered by saejin 4 · 0⤊ 1⤋
a1 = 4
a2 = 2(4) + 3 = 11
a3 = 2(11) + 3 = 25
a4 = 2(25) + 3 = 53
D. 53
2007-12-26 12:16:41 · answer #4 · answered by Anonymous · 0⤊ 0⤋
a1 is just the name that's being given to the first number in the sequence, so in this case, the sequence starts with 4, then continues with the next, a2 (read, 'the second term of the sequence "a"') being 2*4 + 3, and so on...
2007-12-26 12:17:10 · answer #5 · answered by Anonymous · 0⤊ 0⤋
I believe the answer is D 53. Think a1, a2, a3, a4 as variables like w,x,y,z. So you are looking for the a4, which is z. Given that w = 4, substitute and solve for a2 or x and then solve for y and then solve for z and you get 53.
2007-12-26 13:40:49 · answer #6 · answered by Anonymous · 0⤊ 0⤋
this is the last thing we covered in algebra 2..i got an F in the class so i'm probalby wrong lol but heres what i think
a1's value is 4
a2=2 times the value of a1 plus 3...2x4+3=11
a3=2 times the value of a2 plus 3...2x11+3=25
a4=2 times result of a3 (25) plus 3= 53
D is the answer!
2007-12-26 12:20:59 · answer #7 · answered by G 1 · 0⤊ 0⤋
a1,a2,a3 and a4 are all variables. The same way you would use x or y. Ifg a1=4 then a2=2x4+3 or 11.Then a3=2x11+3 or 25.Then a4=2x25+3 or 53 and "d" is your answer.
2007-12-26 12:23:10 · answer #8 · answered by coxdpcl22 2 · 0⤊ 0⤋
In the second equation, replace the a1 with 4, and you get a2 = 11.
In the third equation, replace a2 with 11 to solve for a3. Plug this answer into the fourth equation to replace the a3 to solve for a4.
2007-12-26 12:16:32 · answer #9 · answered by Citizen for President 2 · 0⤊ 0⤋
solve a2 first: a2 = 2*4 + 3 = 11
then solve a3: a3 = 2*11 + 3 = 25
then solve a4: a4 = 2*25 + 3 = 53
2007-12-26 12:15:00 · answer #10 · answered by casey2542 2 · 0⤊ 0⤋