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## SS2: MATHEMATICS - 2ND TERM

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Lesson 1, Topic 2
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# Arithmetic Progression (A.P)

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#### Topic Content:

• Definition of Arithmetic Progression

### What is Arithmetic Progression?

Arithmetic Progression is a sequence in which the difference between consecutive terms is constant. This constant is known as the common difference.

The common difference, d, can be found by subtracting the 1st term from the second term or the second term from the third term.

The general form of an A.P is given as

a, a + d, a + 2d, a + 3d, a + 4d…

where a = 1st term and d = common difference.

It is important to note that the coefficient of “d” is always one less than the number of the term. The nth term is denoted byÂ

$$\scriptsize T_n = a \: + \: (n\:-\:1)d$$

### Example 1.2.1:

The first and last terms of an A.P. are -3 and 145 respectively. If the common difference is 4, find theÂ

i. 12th term
ii. 25th term
iii. The number of terms in the A.P

Solution:

i. a = -3, d = 4, n = 12

Tn = a + (n – 1) d

T12 = -3 + (12 – 1) Ã— 4

= -3 + 11 Ã— 4

= -3 + 44

T12 = 41Â

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