Question

Write the nth term of the following sequence in terms of the first term of the sequence.

1, 8, 15, 22, . . .

Answer 1

`\bold{a_n=7n-6}`

Explanation:

a₁ = 1

a₂ = 8 = 1 + 7 = a₁ + 7

a₃ = 15 = 1 + 7 + 7 = a₁ + 7×2

a₄ = 22 = 1 + 7 + 7 + 7 = a₁ + 7×3

Therefore:

`a_n=1+7(n-1)=1+7n-7\\\\a_n=7n-6`