Question

What is the first, fourth, and tenth terms of the arithmetic sequence `A(n) = -6 + (n-1)(?6)`?

Answer 1

a) First Term `color(red)(a_1 = -6`

b) Fourth term `color(blue)(a_4 = -6 + (4-1) * 6 = 12`

c) Tenth Term `color(green)(a_(10) = -6 + (10-1) * 6 = 48`

Explanation:

`A_n = -6 + (n-1) * 6` Eqn (1)

Standard for of an Arithmetic Sequence for the `n^(th)` term is given by the formula,

`A_n = A_1 + (n-1) * d` Eqn (2),

where `a_1` first term & `d` the common difference.

Comparing Eqns (1), (2)

`a_1 = -6, d = 6`

a) First Term `a_1 = -6`

b) Fourth term `a_4 = -6 + (4-1) * 6 = -6 + (3 * 6) = 12`

c) Tenth Term `a_(10) = -6 + (10-1) * 6 = -6 + 54 = 48`