Find the three terms in a sequence. write the rule for finding the nth term
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Example Questions
Algebra 1 Help » Functions and Lines » Sequences » How to find the nth term of an arithmetic sequence
Find The Nth Term Of An Arithmetic Sequence : Example Question #1
The first term of an arithmetic sequence is 10; the fifth term is 38. What is the second term?
Possible Answers:
24
20
18
17
12
Correct answer:
17
Explanation:
To find the common difference d, use the formula a1+4d=a5.
For us, a1 is 10 and a5 is 38.
10+4d=38
Now we can solve for d.
4d=28
d=7
Add the common difference to the first term to get the second term.
a2=a1+d=10+7=17
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Find The Nth Term Of An Arithmetic Sequence : Example Question #2
The sum of the first three terms of an arithmetic sequence is 111 and the fourth term is 49. What is the first term?
Possible Answers:
31
37
It cannot be determined from the information given.
13
24
Correct answer:
31
Explanation:
Let d be the common difference, and let x be the second term. The first three terms are, in order, x−d,x,x+d.
The sum of the first three terms is (x−d)+x+(x+d)=111.
x+x+x+d−d=3x=111
x=1113=37
Now we know that the second term is 37. The fourth term is the second term plus twice the common difference: x+2d. Since the second and fourth terms are 37 and 49, respectively, we can solve for the common difference.
x+2d=37+2d=49
2d=12
d=6
The common difference is 6. The first term is x−d=37−6=31.
Answer:
Let the three terms in a sequence be
a-b , a , a+b
Taking the above sequence you can easily find the three terms.
The rule for finding the nth term is
a nth term = a+(n-1)d
where a is first term , n is no. of terms, d is common differenc .