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Math  /  Algebra

QuestionEnter the first five terms of the following recursively defined sequence. a1=1;an=an−1+n,n≥2a1=□\begin{array}{l} a_{1}=1 ; a_{n}=a_{n-1}+n, n \geq 2 \\ a_{1}=\square \end{array} □\square a2=a_{2}= □\square a3=a_{3}= □\square a4=a_{4}= □\square a5=□a_{5}=\square

Studdy Solution

STEP 1

1. The sequence is defined recursively, meaning each term is defined based on the previous term.
2. The first term a1 a_1 is given as 1.
3. For n≥2 n \geq 2 , each term is calculated using the formula an=an−1+n a_n = a_{n-1} + n .

STEP 2

1. Identify the first term of the sequence.
2. Calculate the subsequent terms using the recursive formula.

STEP 3

Identify the first term of the sequence:
Given: a1=1 a_1 = 1

STEP 4

Calculate the second term using the recursive formula:
a2=a1+2 a_2 = a_1 + 2 a2=1+2 a_2 = 1 + 2 a2=3 a_2 = 3

STEP 5

Calculate the third term using the recursive formula:
a3=a2+3 a_3 = a_2 + 3 a3=3+3 a_3 = 3 + 3 a3=6 a_3 = 6

STEP 6

Calculate the fourth term using the recursive formula:
a4=a3+4 a_4 = a_3 + 4 a4=6+4 a_4 = 6 + 4 a4=10 a_4 = 10

STEP 7

Calculate the fifth term using the recursive formula:
a5=a4+5 a_5 = a_4 + 5 a5=10+5 a_5 = 10 + 5 a5=15 a_5 = 15
The first five terms of the sequence are: a1=1 a_1 = 1 a2=3 a_2 = 3 a3=6 a_3 = 6 a4=10 a_4 = 10 a5=15 a_5 = 15

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