Consider the sequence defined by a_n = n(n+1)/2. Is this a recursive or explicit
ID: 3006993 • Letter: C
Question
Consider the sequence defined by a_n = n(n+1)/2. Is this a recursive or explicit equation? Explain why. Using the formula, list the first 4 terms of the sequence (starting with n=1). This problem is similar to examples 4-7 and problems 1.3.7-1.3.14. Example 4 The recursive formula c_1 = 5, c_n = 2c_n-1, 2 le n le 6, defines the finite sequence 5, 10,20,40, 80,160. Example 5 The infinite sequence 3, 7, 11, 15, 19, 23,... can be defined by the recursive formula d_1 = 3, d_n = d_n-1 + 4. Example 6 The explicit formula s_n = (-4)^n, 1 le n, describes the infinite sequence -4,16, -64, 256,.... Example 7 The finite sequence 87, 82, 77, 72, 67 can be defined by the explicit formula t_n = 92 - 5_n, 1 le n le 5. Example 8 An ordinary English word such as "sturdy" can be viewed as the finite sequence s, t, u, r, d, y composed of letters from the ordinary English alphabet. In examples such as Example 8, it is common to omit the commas and write the word in the usual way, if no confusion results. Similarly, even a meaningless word such as "abacabcd" may be regarded as a finite sequence of lengthe 8. Sequences of letters or other symbols, written without the commas, are also referred to as stFind thegs.Explanation / Answer
It is an explicit equation since once an n is given:a_n can be determined
a_1=1(1+1)/2=1
a_2=2(2+1)/2=3
a_3=3(3+1)/2=6
a_4=4(4+1)/2=10