Question

Determine the A.P whose third term is 16 and the 7th term exceeds the 5th term by 12 (2m)

Answer 1

Answer:
`a_n=6n-2`

Explanation:

a₁, ____, 16, ____, a₅, _____, a₇

The difference of a₇ and a₅ is 2d (two steps to the next term).

It is given that 2d = 12 --> d = 6

We can subtract 6 from a₃ to find a₁

a₁ = 4, 10, 16, ____, a₅, _____, a₇

Input a₁ = 4, d = 6 into the explicit formula for an arithmetic equation.

`a_n=a_1+d(n-1)\\\\a_n=4+6(n-1)\\\\a_n=4+6n-6\\\\\large\boxed{a_n=6n-2}`