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
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
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