Sequences and Series Exercise 1
Question:
an=n(n^2+5)/4
Answer:
Step 1: Expand the expression to get ‘an = n^3 + 5n/4.’
Step 2: Multiply both sides of the equation by 4 to get ‘4an = 4n^3 + 20n.’
Step 3: Subtract 4n^3 from both sides of the equation to get ‘4an  4n^3 = 20n.’
Step 4: Divide both sides of the equation by 4 to get ‘an = n^2 + 5/4.’
Question:
an=n(n−2)/(n+3);a20
Answer:
Step 1: Substitute n = 20 in the given equation. an=20(20−2)/(20+3);a20
Step 2: Simplify the equation. an=380/(23);a20
Step 3: Calculate the value of an. an = 16.5217;a20
Question:
an =n/(n+1)
Answer:
Step 1: Multiply both sides of the equation by (n + 1): an(n + 1) = n
Step 2: Isolate the n on the left side of the equation: an(n + 1)  n = 0
Step 3: Factor the left side of the equation: n(an + 1) = 0
Step 4: Set each factor equal to zero: n = 0 an + 1 = 0
Step 5: Solve each equation: n = 0 a = 1
Question:
an=n^2/2^n;a7
Answer:
a7 = (7^2)/2^7
a7 = (49)/128
a7 = 0.3828125
Question:
a1=3,an=3a(n−1)+2 for all n>1
Answer:
Step 1: Calculate a2: a2 = 3a(2−1)+2 a2 = 3a(1)+2 a2 = 3(3)+2 a2 = 11
Step 2: Calculate a3: a3 = 3a(3−1)+2 a3 = 3a(2)+2 a3 = 3(11)+2 a3 = 35
Question:
a1=−1,an=(an−1)/n,n≥2
Answer:
Step 1: a1 = 1
Step 2: a2 = (a1)/2 = (1)/2 = 1/2
Step 3: a3 = (a2)/3 = (1/2)/3 = 1/6
Step 4: a4 = (a3)/4 = (1/6)/4 = 1/24
Step 5: a5 = (a4)/5 = (1/24)/5 = 1/120
Step 6: a6 = (a5)/6 = (1/120)/6 = 1/720
Step 7: a7 = (a6)/7 = (1/720)/7 = 1/5040
Step 8: a8 = (a7)/8 = (1/5040)/8 = 1/40320
Step 9: a9 = (a8)/9 = (1/40320)/9 = 1/362880
Step 10: a10 = (a9)/10 = (1/362880)/10 = 1/3628800
Question:
an=(−1)^(n−1)5(n+1)
Answer:
Step 1: Simplify the exponent: an = (1)^(n1)5(n+1)
Step 2: Rewrite the expression using the power rule: an = (1) * 5 * (n^2 + n)
Question:
an=(−1)^(n−1)n^3;a9
Answer:

Replace ’n’ with ‘9’ in the equation: an=(−1)^(9−1)9^3

Simplify the equation: an=(−1)^8*9^3

Calculate the power of 9: an=(−1)^8*729

Calculate the power of 1: an=1*729

Multiply the two numbers: an=729
Question:
If a1=a2=2,an=a(n−1)−1(n>2) then a5 is ? A : 1 B : −1 C : 0’ D : −2
Answer:
Answer: B (1) Step 1: a1=a2=2 Step 2: an=a(n−1)−1, for n>2 Step 3: a5=a4−1 Step 4: a4=a3−1 Step 5: a3=a2−1 Step 6: a2=2 Step 7: a3=1 Step 8: a4=0 Step 9: a5=−1
Question:
an=2^n
Answer:
 a1=2^1
 a2=2^2
 a3=2^3
 a4=2^4
 a5=2^5
 a6=2^6
 a7=2^7
 a8=2^8
 a9=2^9
 a10=2^10
Question:
an=4n−3;a17,a24
Answer:
a17 = 4(17)  3 = 67
a24 = 4(24)  3 = 95
title: “Exercise 1” parent: “09 Sequences and Series” draft: false
Question:
The fibonacci sequence is defined by a1=1=a2 ;
an=a(n−1)+a(n−2) for n>2.
Find (an+1)/an, for n=1,2,3,4,5.
A : 1,2,3/2 ,5/3 and 8/5
B : 1,2,3/2,4 and 8
C : 3,4,9/2, 5 and 8
D : 1,2,3/2, 6 and 9
Answer:
Answer: A
Question:
an=(2n−3)/6
Answer:
Step 1: Multiply both sides of the equation by 6.
6an = 2n  3
Step 2: Add 3 to both sides of the equation.
6an + 3 = 2n
Step 3: Divide both sides of the equation by 2.
(6an + 3)/2 = n