## ARITHMETIC SERIES WORKSHEET SOLUTION1

Arithmetic series worksheet solution1 :

Here we are going to see solution of each questions from the arithmetic series worksheet.

(1) Find the sum of first 75 positive integers

Solution :

To find the sum of first 75 positive integers first let us write the series

1 + 2 + 3 + ..........+ 75

Total number of terms in the series is 75 so n = 75

Sn = (n/2) (a+L)

=  (75/2) (1+75)

=  (75/2) (76)

=  75 x 38

=  2850

(ii) 125 natural numbers

Solution :

To find the sum of first 125 positive integers first let us write the series

1 + 2 + 3 + ..........+ 125

Total number of terms in the series is 125 so n = 125

Sn = (n/2) (a+L)

=  (125/2) (1+125)

=  (125/2) (126)

=  125 x 63

=  7875

(2) Find the sum of first 30 terms of an A.P whose nth term is 3 + 2 n

Solution :

nth term = 3 + 2 n

t n = 3 + 2 n

From the general term (tn) we are going to find first and last term of the arithmetic series for that first we have to apply 1 for n to get the value of first term (a) and we have to apply 30 for n to get the last term (L). Because we have only 30 terms in this series.

n = 1

t 1 = 3 + 2 (1)

t 1 = 5

a = 5

n = 30

t₃₀ = 3 + 2(30)

t₃₀ = 3 + 60

t₃₀ = 63

L = 63

Now we have to find S₃₀ for that we have to use the formula

Sn = (n/2) [a+L]

S₃₀ = (30/2) [5 + 63]

=  15 [5 + 63]

=  15 [68]

S₃₀ = 1020

(3) Find the sum of each arithmetic series

(i) 38 + 35 + 32 + .......... + 2

Solution :

First we have to know that how many terms are there in the above series.

a = 38    d = t₂ - t₁          L = 2

d = 35-38

= -3

n  =  [(L-a)/d] + 1

=  [(2-38)/(-3)] + 1

=  [(-36)/(-3)] + 1

=  12 + 1

n  =  13

Sn  =  (n/2) (a+L)

=  (13/2) (38 + 2)

=  (13/2) (40)

=  (13) (20)

=  260

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