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MATHEMATICS TUTORIAL

ARITHMETIC PROGRESSION PROBLEM AND SOLUTIONS

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ARITHMETIC PROGRESSION PROBLEM

There is always a general formula governing some solving. The general formula of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n – 1) d, where Tn = nth term and a = first term. … The sum of n terms is also equal to the formula where l is the last term.

1. What is the sum of 20 terms of 31/4 + 61/4 + 81/4 + …

Solution

This is the formula used in solving the sum of an Arithmetic Progression. Sn = n/2 [ (2n + (n – 1) ]d

Sn = n/2 [ (2n + (n – 1) ]d

Sn = 20/2 [ 2 x 15/4 + (20 – 1)] 15/2

Sn = 10 [ 15/2 + (19)] 15/2

Sn = 10 (15/2 + 95/2)

Sn = 10 (15 + 95)/2

Sn = 10 x 110/2

Sn = 10 x 55

Sn = 550.

Arithmetic Progression

Arithmetic Progression

 

2. Eight wood poles are to be used for pillars and the length of the poles form an Arithmetic progression (A.p) If the second pole is 2m and the sixth term is 5m, give the length of the poles.

Solution

This is the formula used in solving the nth term of an Arithmetic Progression Tn = a + (n – 1)d

Tn = a + (n – 1)d

T2 = a + ( 2 – 1)d = 2

T2 = a + (1)d = 2

T2 = a + d = 2         equation 1

T6 = a + ( n – 1)d = 5

T6 = a + ( 6 – 1)d = 5

T6 = a + ( 5)d = 5

T6 = a + 5d = 5      equation 2

 

therefore group them i.e

T2 = a + d = 2         equation 1

T6 = a + 5d = 5      equation 2

subtract equation eq 1 from eq 2

4d = 3

divide both side by 4

4d/4 = 3/4

d = 0.75

substitute fo a using eq. 1

a + d = 2

a + 0.75 = 2

a = 2 – 0.75

a = 1.25

now we have gotten out first time a = 1.25 and common difference d = 0.75 so we want to find the Eight wooden poles

Tn = a + (n – 1)d

T1 = 1.25 + ( 1 -1)0.75

T1 = 1.25 + ( 0)0.75

T1 = 1.25 + 0

T1 = 1.25m

Second term

T2 = 1.25 + ( 2 -1)0.75

T2 = 1.25 + ( 1)0.75

T2 = 1.25 + 0.75

T2 = 2m

Third term

T3 = 1.25 + ( 3 -1)0.75

T3 = 1.25 + ( 2)0.75

T3 = 1.25 + 1.5

T3 = 2.75m

fourth term

T4 = 1.25 + ( 4 -1)0.75

T4 = 1.25 + ( 3)0.75

T4 = 1.25 + 2.25

T4 = 3.5m

Fifth term

T5 = 1.25 + ( 5 -1)0.75

T5 = 1.25 + ( 4 )0.75

T5 = 1.25 + 3

T5 = 4 . 25m

Sixth term

T6 = 1.25 + ( 6 -1)0.75

T6 = 1.25 + ( 5)0.75

T6 = 1.25 + 3.75

T6 = 5m

Seventh term

T7 = 1.25 + ( 7 -1)0.75

T7 = 1.25 + ( 6)0.75

T7 = 1.25 + 4.5

T7 = 5.75

Eight Term

T8 = 1.25 + ( 8-1)0.75

T8 = 1.25 + (  7)0.75

T8 = 1.25 + (  7)0.75

T8 = 1.25 + 5.25

T8 = 6.5m

So that is the final answer for that questions that was solved,  Nkedugist  produce those answers to that questions that was properly and carefully solved but if you think that is not the answer you might as well solve yours on the comment box for the audience to see which we be approved.

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