Question

Find a(12) and a(n) for the ARITHMETIC sequence

a(14)=46 , a(16)=58

Answer 1

For an arithmetic sequence, a(n) = a(1) + d*(n-1)
So for n = 14, a(14) = a(1) + 13d = 46
For n = 16, a(16) = a(1) + 15d = 58
Subtracting the first equation from the second gives: 2d = 12
Dividing by 2: d = 6
Substituting into the 1st equation: a(1) + 13*6 = 46
a(1) = -32
Therefore, a(12) = a(1) + 11d = -32 + 11(6) = 34
a(n) = -32 + 11d