Answer:
Tn = 34-3n
Explanation:
The formula for calculating the nth term of an arithmetic sequence is given as;
Tn =
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