Find the indicated terms in each of the following sequences whose nth terms are:
(i) an=5n-4; a₁₂ and a₁₅
(ii) an3n-2/4n+5;a₇ and a₈
(iii) an=n(n-1)(n-2);a₅ and a₈
(iv) an=n(n-1)(2-n)(3+n);a₁,a₂,a₂
(v)an=(-1)ⁿ n;a₃,a₅,a₈
Answers
Find the indicated terms in each of the following sequences whose nth terms are:
(i) an=5n-4; a₁₂ and a₁₅
a(n) = 5n - 4
a(12) = 5 (12) - 4 = 60 - 4 = 56
a(15) = 5 (15) - 4 = 75 - 4 = 71
(ii) an3n-2/4n+5;a₇ and a₈
a(n) = 3n - 2 / 4n + 5
a(7) = 3 (7) - 2 / 4 (7) + 5 = 19 / 33
a(8) = 3 (8) - 2 / 4 (8) + 5 = 22 / 32 = 11 / 16
(iii) an=n(n-1)(n-2);a₅ and a₈
a(n) = n (n-1) (n-2)
a(5) = 5 (5-1) (5-2) = 5 (4) (3) = 60
a(8) = 8 (8-1) (8-2) = 8 (7) (6) = 336
(iv) an=n(n-1)(2-n)(3+n);a₁,a₂,a₂
a(n) = n (n-1) (2-n) (3+n)
a(1) = 1 (1-1) (2-1) (3+1) = 1 (0) (1) (4) = 0
a(2) = 2 (2-1) (2-2) (3+2) = 2 (1) (0) (5) = 0
a(2) = 2 (2-1) (2-2) (3+2) = 2 (1) (0) (5) = 0
(v)an=(-1)ⁿ n;a₃,a₅,a₈
a(n) = (-1)^n (n)
a(3) = (-1)^3 (3) = -1 (3) = -3
a(5) = (-1)^5 (5) = -1 (5) = -5
a(8) = (-1)^8 (8) = 1 (8) = 8
Answer:
Step-by-step explanation:
1) an=5n-4;a12 and a15
a(n)=5n-4
a(12)=5(12)-4
a(12)=60-4
a(12)=56
a(15)=5(15)-4
a(15)=75-4
a(15)=71
2) an=3n-2/4n+5;a7 and a8
a(n)=3n-2/4n+5
a(7)=3(7)-2/4(7)+5
a(7)=21-2/28+5
a(7)=19/33
a(8)=3(8)-2/4(8)+5
a(8)=24-2/32+5
a(8)=22/37
3) a(n)=n(n-1)(n-2);a5 and a8
a(n)=n(n-1)(n-2);a5anda8
a(5)=5(5-1)(5-2)
a(5)=5(4)(3)
a(5)=60
a(8)=8(8-1)(8-2)
a(8)=8(7)(6)
a(8)=336
4) a(n)=n(n-1)(2-n)(3+n);a1,a2,a2
a(n)=n(n-1)(2-n)(3+n)
a(1)=1(1-1)(2-1)(3+1)
a(1)=1(0)(1)(4)
a(1)=0
a(2)=2(2-1)(2-2)(3+2)
a(2)=2(1)(0)(5)
a(2)=0
a(2)=2(2-1)(2-2)(3+2)
a(2)=2(1)(0)(5)
a(2)=0
5) a(n)=(-1)^n n;a3 ,a5,a8
a(n)=(-1)^n(n)
a(3)=(-1)^3(3)
a(3)=-1(3)
a(3)=-3
a(5)=(-1)^5(5)
a(5)=-1(5)
a(5)=-5
a(8)=(-1)^8(8)
a(8)=1(8)
a(8)=8
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