A few days ago
Solve using substitution?
7. Suppose for an arithmetic sequence t4 = 2 and t40 = -106. Find the equation for the nth term.
-Arithmetic formula: tn = t1 + (n-1)d
2 = t1 + (4-1)d
2 = t1 + 4d – d
2 = t1 + 3d
2 – 3d = t1
-106 = t1 + (40-1)d
-106 = t1 + 40d – d
-106 = t1 + 39d
-106 – 39d = t1
t1 = -106 – 39d
t1 = 2 – 3d
Solve by substitution?
Thanks in advance,
Top 1 Answers
A few days ago
Favorite Answer
t1 = -106 – 39d …(1)
t1 = 2 – 3d …(2)
Substitute for t1 from the first equation in the second. In other words, equate the right hand sides, as they are both equal to t1.
2 – 3d = -106 – 39d
36d = -108
d = -108 / 36 = -3.
Putting this value in (2):
t1 = 2 – (-9) = 11.
Hence the n-th term is:
tn = 11 – 3(n – 1).
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