Question

Write an explicit and a recursive formula for the sequence.
6, 14, 22, 30, 38, ..
Write an explicit formula.

Answer 1

Answer:

• Recursive: a₁ = 6, aₙ = aₙ₋₁ + 8
• Explicit: aₙ = 8n - 2

Step-by-step explanation:

Given sequence:

• 6, 14, 22, 30, 38, ..

We observe that:

• The sequence is a AP
• The first term a₁ = 6
• Common difference is d = 8

The recursive formula:

• a₁ = 6, aₙ = aₙ₋₁ + 8

The explicit formula:

• aₙ = a₁ + (n - 1)d = 6 + (n - 1)*8 = 8n - 2

Answer 2

It's an arithmetic progression

• First term a=6
• Common difference=d=14-6=8

Explicit formula

• a_n=a+(n-1)d
• a_n=6+8(n-1)
• a_n=8n-2