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Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.

User Kiechlus
by
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1 Answer

5 votes

Answer:

Tn = 34-3n

Explanation:

The formula for calculating the nth term of an arithmetic sequence is given as;

Tn =
a+(n-1)d

a is the first term

n is the number of terms

d is the common difference

If two terms of an arithmetic sequence are a12=70 and a30=124 then;

T12 = a+(12-1)d = 70

T12 = a+11d = 70...(1)

T30 = a+(30-1)d = 124

T30 = a+29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d;

Taking the difference of both equation we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d=3 into equation 1 to get the value of 'a' we have;

a+11(3) = 70

a+33=70

a = 70-33

a = 37

To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3

Tn = 37+(n-1)3

Tn = 37+3n-3

Tn = 34-3n

This gives the required nth term

User Niel
by
8.3k points
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