**Practical problems in arithmetic sequence :**

An arithmetic series is a series whose terms form an arithmetic sequence.

Here we are going to see some practical problems based on the topic arithmetic sequence.

**Problem 1 :**

A TV manufacturer has produced 1000 TVs in the seventh year and 1450 TVs in the tenth year. Assuming that the production increases uniformly by a fixed number every year, find the number of TVs produced in the first year, find the number of TVs produced in the first year and 15th year.

**Solution :**

Number of TVs produced in the seventh year = 1000

Number of TVs produced in the tenth year = 1450

t7 = 1000

t10 = 1450

a + 6 d = 1000 ----- (1)

a + 9 d = 1450 ----- (2)

(1) – (2)

Subtracting second equation from first equation

aaaaaaaaaaaaaaa + 6 d = 1000aaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaa + 9 d = 1450aaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaa(-) (-) (-)aaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaa------------------aaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaa-3d = -450aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaad = -450/(-3) ==> d = 150

Substitute d = 150 in the first equation

a + 6(150) = 1000

a + 900 = 1000

a = 1000 -900

a = 100

Therefore number of TVs produced on the first year is 100

To find number of TVs produced in the 15th year year we have to find the 15th term of the A.P

tn = a + (n-1) d

t15 = 100 + (15-1) 150

t15 = 100 + 14(150)

= 100 + 2100

= 2200

**Problem 2 :**

A man has saved $640 during the first month,$720 in the second month and $800 in the third month. If he continues his savings in this sequence, what will be his savings in the 25th month?

**Solution :**

If we write his saving like a sequence, we will get 640,720,800,………… to get 25th month savings

From this we have to find the 25th term of the sequence

a = 640 d = t2 – t1

= 720- 640

= 80

tn = a + (n-1) d

t25 = 640 + (25 - 1) 80

= 640 + 24 (80)

= 640 + 1920

= 2560

Hence, he saves $2560 in the 25th month

**Problem 3 :**

A person has deposited $25000 in an investment which yields 14% simple interest annually. Do these amounts (principal + interest) form an A.P? If so, determine the amount of investment after 20 years.

**Solution :**

Simple interest = PNR/100

= (25000 x 1 x 14)/100

= 3500

Amount = principal + interest

= 25000 + 3500

= 28500

Amount at the end of the first year = 28500

Amount at the end of second year = 28500 + 3500

= 32000

Amount at the end of third year = 32000 + 3500

= 35500

28500,32000,35500.,………………….

This is the arithmetic sequence. To find the amount of investment after 20 years we need to find 20th term

tn = a +(n - 1) d

a = 28500 d = 32000 – 28500

= 3500

t20 = 28500 + (20 - 1) 3500

= 28500 + 19 (3500)

= 28500 + 66500

= 95000

After having gone through the stuff given above, we hope that the students would have understood "Practical problems in arithmetic sequence".

Apart from the stuff given above, if you want to know more about "Practical problems in arithmetic sequence", please click here

Apart from the stuff "Practical problems in arithmetic sequence" 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**