• The sum of the first n terms of the sequence, denoted by Sₙ is called partial sum of the sequence.

If a₁,a₂,a₃,a₄,…,aₙ…   are the terms of the sequence, then

S₁=a₁                                   S₁   is the first term of the sequence.

S₂=a₁+a₂                              S₂ is the first two terms of the sequence

S₃=a₁+a₁+a₃                         S₃ is the first three terms of the sequence

S₄=a₁+a₂+a₃+a₄                    S₄ is the first four terms of the sequence

  ⋮                                               ⋮

Sₙ=a₁+a₂+a₃+a₄+…+aₙ           Sₙ is the first n terms of the sequence

1. Find the sum of the first six  prime natural numbers.

2. Find the sum of the first 8 natural numbers that are multiples of 4.

 3. Given the general term, aₙ  = 2n +3 , find s₆

4. Given a general term aₙ  =1/(n(n+1))  , find the sum of first 

a) 99 terms

b) n terms

 

 

1. Find the sum of

a. The first five odd natural numbers

b. the first ten odd natural numbers

2. Find the sum of the following sequences to the given term

a. aₙ  = 4n -3,  S₅   

b. aₙ  = 3 - 5n, S₈ 

c. aₙ = n²+1,  S₆

3. Given the general term aₙ  =2/(n²+5n+6), find the sum of the first n terms.

4.Given the general term aₙ  =n/(n+1)-(n+1)/(n+2) "," where n is a positive integer; FindS₆,S₁₀,S₂₀,S₁₀₀ Can you give a formula forSₙ?

 

 

  • Sigma notation is the method used to write out a long term sum in a concise way.

  • We use sigma notation for writing finite and infinite numbers of terms in a sequence.

  • The sum is denoted by the sigma notation using the Greek letter S (sigma)

  • If a_1,a_2,a_3,a_4,…,a_n…are the terms of the sequence, then

         S_n=a_1+a_2+a_3+a_4+…+a_n

                                 

1. Express the following sigma notation in the form of sum

  

 

 

1. Express the following sigma notations in the form of a  sum

 

 

 

 

2. Express the following using sigma notation.

a. 2²+4²+6²+8²+10²+12²

b. 4 + 7 + 10 + 13 + … + 52

c. 1 + 3 + 5 + 7 + … + 51

3. Use the sigma notation to represent the sum of the first n terms of the given sequences.

a. 4, 8, 12, …, 4k, … for n=5.

b.  2, 5, 8, …, 3k-1, … for n = 8.

c. 2, 8, 18, …, 2k²  , … for n=7.

d. 7, 9, 11, …, (2k + 5), … for n =10 

 

 

Let aₙand bₙare a sequences and c is a constant. Then  

Evaluate the following sigma notation.

Given a sequence for which aₙ=4n³

a. s₄

b. s₆

 

 

1. Evaluate the following sigma notations.

 

 

The sum of the first n  consecutive natural number is

Find the sum of the first      

a) 50 natural numbers

b) 300 natural numbers

1. Find the sum of the first

a. 30 natural numbers.

b. 99 natural numbers

c. 200 natural numbers

2. If the sum of the first natural numbers is 3240, what is the value of n?

 

 

  • The sum Sₙ of the first n terms of an arithmetic sequence with first term  A₁ and common difference d is:

       

The formula can also be written as

This alternative formula is useful when the first and last term are known.

Find the sum of the first 20 terms of the sequence whose general term is Aₙ=7n

If the first term of an arithmetic sequence is 6 and the common difference is 3, then find the sum of the first 30 terms.

1) Find the partial sum of the following arithmetic sequences:

a. A₁=2  and   last term A₁₀=21

b. A₁=40  and  last term A₂₆=0

2. find the sum of the following arithmetic sequences:

a) A₁=2, d=3, n=10

b) A₁ = 30, d= -5, n=12

 

 

Find the sum S₆, of arithmetic sequence whose 2nd term is 3 and 6th term is 27. 

Find the sum of integers from 1 to 200 that are divisible by 20.

1. Find S₅ of the arithmetic sequence whose 3rd term is 5 and 5th term is 11

2. Given the sum of an arithmetic sequence is S₈=120 and A₁=1 find A₈ and Aₙ

3. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

4. Find the sum of odd  integers from 1 to 2001.

 

 

Find the sum of the following sequences.

a. {3,9,27,81,243}

b. {1, ³/₂, ⁹/₄, ²⁷/₈ ,⁸¹/₁₆}

Find the sum of 1st to nth of the following geometric sequences.

a) G₁=3, r=2  

b) G₁=1,r = ½

c) 1,3,9,27,81,…

The sum of the first three terms of a geometric sequence is 13, and the sum of the 4th to 6th terms is 104. Find the first term and the common ratio.

 

 

1. The sum of the first three terms of a geometric sequence is 9, and the sum from the 4th to 6th term is -18. Find the first term and common ratio.


2.  How many terms of the sequence: 3,3/2,¾, ⅜ ,.... Are needed to give the sum 3069/512 ?

3.  Find the sum to indicated number of terms in each of the geometric sequence in questions a to d:

a. 0.15, 0.015, 0.0015, … n terms.

b. 1, -a,a²,-a³ , … n terms (if a = -1).

d. x³, x⁵, x⁷, … n terms (if x= + 1)

Last modified: Tuesday, 21 October 2025, 10:53 AM