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Arithmetic Progression (AP) [Mathematics JAMB Tutorial]

Today on our JAMB UTME Free Tutorial, will treat mathematics and our topic is Arithmetic Progression (AP); SEQUENCE AND SERIES.

As we said in the introduction, we will be teaching you ARITHMETIC PROGRESS (AP). Since you can’t talk about AP without starting mentioning SEQUENCE and SERIES, we will start by explaining those terms.

Before we proceed, please TAKE NOTE of the following:

  • We strongly recommend you take your time and read this topic. You can read it again and again.
  • Make sure you attempt all the exercises on this page. Use the comment box to tell us the answers.
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Now let’s start the tutorial for today:

In a case where numbers are presented in a given array or in an orderly manner, such set of numbers is regarded as SEQUENCE.

EXAMPLE:

  • 1,2,3,4…
  • 2,4,6,8,10…
  • -3,-2,-1…

Also, when the summation of a series is taken, the process is called SERIES

EXAMPLE:

  • 1+2+3+4+…
  • 2+4+6+8+10+…

ARITHMETIC PROGRESSION (AP)

AP is a form of sequence in which each term or preceding number is obtained by the addition of a certain number called the COMMON DIFFERENCE.

EXAMPLE 2:

Examine the pattern of the AP below

  • 7,9,11,13,15…

SOLUTION

TermPattern
7 
9= 7 + 2
11= 9 + 2
13= 11 + 2
15= 13 + 2

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Nth TERM OF AN AP

The nth term of an arithmetic progression is usually donated as “a” and its common difference by “d” while the last term of an AP may be denoted as “n”

We can understand this better using example 2 above and we can have that:

solution to ap sequence eg1

In Summary, the general term of an AP is given as:

  • Tn = a +  (n  –  1) d

EXAMPLE 3

Find the 4th term of a AP whose first term is 2 and common difference is 0.5

SOLUTION:

Tn = a + (n – 1)d………………(1)

Here, n=4, a=2, d= 0.5

Substituting (1) above we have

T4 = 2 + (4 – 1) 0.5

= 2 +(3)0.5

= 2+1.5

 = 3.5

SUM OF AN AP

The sum of an AP refers to the addition of all the terms mentioned or required in a given AP. It is usually donated by Sn . The formulae is given by

Sn = n/2 {2a + (n – 1)d}…………….(2) this is used when a, d, and n is given

Sn = n/2 (a + l) ……………………….(3) this is used when the first term and the last term is given.

EXAMPLE 4:

The first and last term of a linear sequence (A.P) are -12 and 40 respectively if the sum of the sequence is 196, find;

  1. The number of the terms
  2. The common difference
  3. The 12th term

Solution 4:

(1) P last and first term is given by;

Sn =n/2(a+L)

196=n/2(-12+40)

196 x 2 = n(28)

196 x 2/28 = n

14 = n

(2) To find d, we apply the general sum formula for AP

Sn = n/2{2a + (n – 1) d}

S14 → 196 = 14/2 { 2(-12) + (14 – 1)d}

196 = 7(-24 + 13d)

196/7 = -24 + 13d

28 + 24 = 13d

52/13 =d

4 = d

(3) Find the 12th term

Tn = a + (n-1)d

T12 = -12 +( 12-1)4

= -12 + (11)4

= -12 +44

T12 =  32

EXERCISES ON AP

  1. If -8, m, n, 19 are in AP. Find (m,n)
    (a) 1, (b) 10 2, 10 (c) 3, 13 (d) 4, 16
  2. The 6th term of an AP is 20 and the 11th term is -5. Find the sum of the first three terms
    (a) 45 (b) 85 (c) 120 (d) 150
  3. Find the nth term of sequence 4, 10, 16, …
    a. 2(3n – 1) b. 2(2 + 3n-1) c. 2n + 2 d. 2(3n + 2)

THINK & ACT : If we can give you this for FREE, imagine what we can give if you pay and join the ALLSCHOOL JAMB Online Lesson. In the lesson, our hardworking tutors ensure they only teach you things that will come out in JAMB, so you’ll score extremely high in JAMB. Click Here to join the ALLSCHOOL JAMB Online Lesson NOW.

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AllSchool Team.

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Henry Potoko

The second term of an a.p is 2 and the 6th term is-14 what is the first term and the 9th term

Ifeanyi promise

Thanks for the tutorial

Kelvin Mwenda

An insect population is growing. In such a way that each new generation is 1.5 times as large as the previous generation.suppose there are 100 insects in the first generation. How many will be there in the fifth generation

Oguguo Chidiebere

ANSWERS TO AP
1. A(1,10)
2.C(120)
3.A (2(3n -1))

Hence the winner for AP is (08078337922)

Oguguo Chidiebere

Also the winner for the exercise will be announced today by 8pm
Thank you and have a great day ahead.

Yusuf

Pls I have a issue with question 1 its not really clear can you explain how to go about it to me

Debby king

Thanks for the tutorial session it was great

Debby king

In this jamb app are we going to use money to activate the app

OPTIMISTIC AENULLAH

This is really superb, thanks so much for the tutorial sessions

08078337922

1,a. 2,c. 3,a

Ijiga Veronica

Thanks for the tutorial 🙏🙏 more wisdom

Ijeoma

Wow nice

Enoch

Please options to the answer, so that one can be sure, thanks very much for the tutorial

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