## Arithmetic Series Worksheet Solution1

In the page arithmetic series worksheet solution1 you 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

S n = (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

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

= (13/2) (38 + 2)

= (13/2) (40)

= (13) (20)

= 260

These are the contents in the page arithmetic series worksheet solution1.

arithmetic series worksheet solution1