Let the sequence an be defined as follows: a1=1,an=an−1+2 for n≥2. $
Find first five terms and write corresponding series.
Get the complete, step-by-step math solution for: "Let the sequence a_{n} be defined as follows: a_{1}=1, a_{n}=a_{n-1}+2 { for } n ≥ 2 . Find first five terms and write corresponding series.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Understand the Sequence Definition
The problem defines a sequence where the first term, a1, is 1. For any subsequent term an (where n is greater than or equal to 2), it is found by adding 2 to the previous term, an−1. This means it's an arithmetic progression.
Step 2: Calculate the First Five Terms
We start with a1=1. To find a2, we add 2 to a1. We continue this process, adding 2 to the previous term, to find a3, a4, and a5.
Step 3: Write the Corresponding Series
A series is the sum of the terms of a sequence. To write the series corresponding to the first five terms, we simply add them together.
Step 4: Calculate the Sum of the Series (Optional)
Although not explicitly asked, we can calculate the sum of the first five terms of the series by adding them up. This sum is 25.