Finite Series Exercises 13.2

Finite Series Exercises 13.2

Today our topic of discussion is Finite Series Exercises 13.2.

Finite Series Exercises 13.2

 

Finite Series Exercises 13.2

 

Exercise 13.2

  1. a, b, c and d are four consecutive terms of an arithmetic series. Which one of the following is true? 

1)b = (c + d)/2

2) a = (b + c)/2

3) c = (b + d)/2

4) d = (a + c)/2

  1. For n∈ N

(i) sum  n = (n²* (n² + 2n + 1))/4

(ii) sum  n² = 1/6 * n(n + 1)(n + 2) 

(iii) sum  n = (n² + n)/2

Which one of the following is true?

1) i and ii

2) i and iii

3) ii and iii

4) i, ii and iii

On the basis of the following series, answer questions 3 and 4.

log_2(log(4)) + log(8) +***

  1. What is the common difference of the series?

1) 2

2) 4

3) log(2)

4) 2log2

  1. Which one is the 7th term of the series?

1) log32

2) log64

3) log128

4) log256

 

 

  1. Find the eighth term of the series 64 + 32 + 16 + 8 +***
  2. Find the sum of the first 14 terms of the series 3 + 9 + 27 +***
  3. Which term of the series 128 + 64 + 32 +*** 1/2 ?
  4. If (2sqrt(3))/9 is the fifth and (8sqrt(2))/81 is the tenth term of a geometric series, find its third term.
  5. Which term of the 1/(√(2)) – 1 + √(2) -*** is 8√(2) ?
  6. If 5 + x + y + 135 is a geometric series, find the value of x and y. 11. If 3 + x + y + z + 243 is a geometric series, find the value of x, y and z.
  7. What is the sum of the first 7 terms of the series 2 – 4 + 8 – 16 +***?
  8. Find the sum of (2n + 1) terms of the series 1 – 1 + 1 – 1 +***
  9. What is the sum of the first 7 terms of the series log(2) + log(4) + log(8) +*** ? 15. What is the sum of the first 12 terms of the series log(2) + log(16) + log(512) +***?
  10. If the sum of n terms of the series 2 + 4 + 8 + 16 +*** is 254, find the value of n.
  11. What is the sum of (2n + 2) terms of the series 2 – 2 + 2 – 2 +*** ?
  12. If the sum of cubes of n natural numbers is 441, find the value of n and find the sum of those n terms.
  13. If the sum of cubes of n natural numbers is 225, find the value of n and find the sum of squares of those n terms. 20. Show that, 1³ + 2³ + 3³ +***+10³ =(1+2+3+***+10)²
  1. If 1³ + 2³ + 3³ +***+n³ 1+2+3+***+n =210, what is the value of n?
  2. An iron-bar with length of one metre is divided into ten-pieces such that the lengths of the pieces form a geometric progression. If the largest piece is ten times than that of the smallest one, find the length in approximate millimetre of the smallest piece.
  3. The first term of a geometric series is a, common ratio r, the fourth term of the series is -2 and the ninth term is 8√2.

1) Express the above information by two equations.

2) Find the 12th term of the series.

3) Find the series and then determine the sum of the first seven terms of the series.

  1. The nth term of a series is 2n – 4.

1) Find the series.

2) Find the 10 th term of the series and determine the sum of the first 20 terms.

3) Considering the first term of the obtained series as the 1st term and the common difference as common ratio, construct a new series and find the sum of the first 8 terms of the series by applying the formula.

 

 

 

  1. An S.S.C. examinee gets his result at 1: 15 p.m. At 1: 20 p.m. 8 students get their results, at 1: 25 p.m 27 students get theirs.

1) As per the stem write down the two patterns.

2) How many students will know their results at exactly 2: 10 p.m.? How many students would be knowing their results by 2: 10 p.m.?

3) When will 6175225 students get their results?

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