**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

S_{n} = (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

S_{n} = (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 :**

n^{th} 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**

- Arithmetic series worksheet
- Special series
- Sequence
- Arithmetic progression
- Arithmetic series
- Geometric progression
- Geometric series

After having gone through the stuff, we hope that the students would have understood "Arithmetic series worksheet solution1"

Apart from the stuff given above, if you want to know more about "Arithmetic series worksheet solution1", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**