If a_1 = 2 and a_n = a_n-1+2 then find the value of a_4

Answer 1

This is an arithmetic sequence defined recursively. You are given the first term of the sequence along with a rule for finding the next term of the sequence.

Given a₁=2.

Than means a₂=a₁+2 = 2+2 = 4.

Then:

a₃=a₂+2 = 4 + 2 = 6

a₄=a₃+2= 6 + 2 = 8.

So the first 4 terms of the sequence are:

2,4,6,8.

This is an arithmetic sequence with a common difference of 2.

To define the sequence explicitly use:

a_n=a₁+(n-1)d

a_n=2+(n-1)2 = 2+2n-2= 2n

In other words to find the nth term of this sequence multiply n by 2.

a₁=2(1)=2

a₂=2(2)=4

a₃=2(3)=6

a₄=2(4)=8

a₄₅₀=2(450) = 900