Question

Write the first 4 terms of an Arithmetic progression where the common

difference ‘d’ is 2.5 and the first term ‘ a ‘ is 2​

Answer 1

AP  ( Arithmetic progression).

 

A list of numbers a1 ,a2, a3  ………….. an is called an arithmetic progression , Is there exists a constant number ‘d’

a2= a1+d

a3= a2+d

a4= a3+d……..

an= an-1+d ………

Each of the numbers in the list is called a term .

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

This fixed  number is called the common difference( d ) of the AP.

General form of an AP.:

a, a+d, a+2d, a+3d…….

Here a is the first term and d is common difference.

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Solution:

(i) Given:a = 10, d = 10

Let the series be a1, a2, a3, a4, a5 …

a1 = a = 10

a2 = a1 + d = 10 + 10 = 20

a3 = a2 + d = 20 + 10 = 30

a4 = a3 + d = 30 + 10 = 40

a5 = a4 + d = 40 + 10 = 50

 the series will be 10, 20, 30, 40, 50 …

First four terms of this A.P. will be 10, 20, 30, and 40.

(ii)Given: a = – 2, d = 0Let the series be a1, a2, a3, a4 …

a1 = a = -2

a2 = a1 + d = – 2 + 0 = – 2

a3 = a2 + d = – 2 + 0 = – 2

a4 = a3 + d = – 2 + 0 = – 2

 the series will be – 2, – 2, – 2, – 2 …

First four terms of this A.P. will be – 2, – 2, – 2 and – 2.

(iii) Given:a = 4, d = – 3Let the series be a1, a2, a3, a4 …

a1 = a = 4

a2 = a1 + d = 4 – 3 = 1

a3 = a2 + d = 1 – 3 = – 2

a4 = a3 + d = – 2 – 3 = – 5

 the series will be 4, 1, – 2 – 5 …

First four terms of this A.P. will be 4, 1, – 2 and – 5.

(iv) Given:a = – 1, d = 1/2Let the series be a1, a2, a3, a4 …a1 = a = -1

a2 = a1 + d = -1 + 1/2 = -1/2

a3 = a2 + d = -1/2 + 1/2 = 0

a4 = a3 + d = 0 + 1/2 = 1/2

the series will be-1, -1/2, 0, 1/2

First four terms of this A.P. will be -1, -1/2, 0 and 1/2.

(v)Given: a = – 1.25, d = – 0.25Let the series be a1, a2, a3, a4 …

a1 = a = – 1.25

a2 = a1 + d = – 1.25 – 0.25 = – 1.50

a3 = a2 + d = – 1.50 – 0.25 = – 1.75

a4 = a3 + d = – 1.75 – 0.25 = – 2.00

 the series will be 1.25, – 1.50, – 1.75, – 2.00 ……..

First four terms of this A.P. will be – 1.25, – 1.50, – 1.75 and – 2.00.---------------------------------------------------------------------------------------------------Hope this will help you...

Answer 2

Answer:

$a_{1} = 2, \: d = 2.5 \\ a_{2} = a_{1} + d = 2 + 2.5 = 4.5 \\ a_{3} = a_{2} + d = 4.5 + 2.5 = 7 \\ a_{4} = a_{3} + d = 7 + 2.5 = 9.5 \\ Therefore, \: the \: first \: four \: terms \: of \: the \: AP \: is \: 2, \: 4.5, \: 7, \: 9.5.$