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)^(n-1)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:

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

2. Simplify the equation: an=(−1)^8*9^3

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

4. Calculate the power of -1: an=-1*729

5. 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:

1. a1=2^1
2. a2=2^2
3. a3=2^3
4. a4=2^4
5. a5=2^5
6. a6=2^6
7. a7=2^7
8. a8=2^8
9. a9=2^9
10. 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