(a) What is true about 2 consecutive terms, a n and a n+1 ? (b) If a n := 20 - 6

Question

(a) What is true about 2 consecutive terms, an and an+1?

(b) If an := 20 - 6n, prove that the sequence is decreasing.

Explanation / Answer

If a(n), where the parenthesis indicate subscript, is a decreasing sequence, then a(n) > a(n+1). Why? Because n+1 indicates that the term a(n+1) is the term that comes after a(n). Since this is a decreasing sequence, the term after a(n) will be less than the value of a(n). Hope this makes sense. Now, to prove that a(n) = 20 - 6n is a decreasing sequence, just find the values of 5 consecutive terms to see if it actually decreases starting from n = 1. n = 1; a(1) = 20 - 6(1) = 14 n = 2; a(2) = 20 - 6(2) = 8 n = 3; a(3) = 20 - 6(3) = 2 n = 4; a(4) = 20 - 6(4) = -4 n = 5; a(5) = 20 - 6(5) = -10 So as you can see the function a(n) = 20 - 6n is indeed a decreasing sequence. Hope this helped you. Please rate if it did. Thanks.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.