Question

Which rule can you use to find the nTH term of an arithmetic sequence in which the common difference is 5 and a12 = 63?

Answer 1

Arithmetic,  nth =  a + (n - 1)d,   common difference, d = 5

a₁₂ = a + (12 -1)d = 63

a + 11d = 63

a + 11*5 = 63

a = 63 - 11*5

a = 63  - 55

a = 8

So the nth term = a + (n - 1)d = 8 + (n - 1)5

8 + 5*(n - 1)

8 + 5n - 5

8 - 5 + 5n

3 + 5n

So nth term = 3 + 5n