Question

find a formula for the nth term in this arithmetic sequence:
a₁ = 28, a₂ = 21, a₃ = 14, a₄ = 7, ...
aₙ = ?n +
hint: the coefficient of n is the common difference.

Explanation:

Step1: Find common difference $d$

$d = a_2 - a_1 = 21 - 28 = -7$

Step2: Identify first term $a_1$

$a_1 = 28$

Step3: Plug into linear arithmetic formula

The arithmetic sequence formula in the form $a_n = dn + c$: substitute $n=1$, $a_1=28$, $d=-7$
$28 = -7(1) + c$
Solve for $c$: $c = 28 + 7 = 35$

Step4: Write final formula

Substitute $d=-7$ and $c=35$ into $a_n = dn + c$

Answer:

$a_n = -7n + 35$