Find the sum :

1^2 + 2^2 + 3^2 +.....324

Write 3+11+19+27+35 using sigma notations.

Find the following sums :

i)1^2+2^2+3^2+....256

ii)1^3+2^3+3^3+...729

Which of the following are Arithmetic Progressions?

a)3,9,15,21....

b)6,13,15,22.....

You may have seen job advertisements in newspapers. They sometimes say 'the pay scale is 10750—300—16750'. Do you know what this means? This means that you will get a basic salary of 10750 in the first year. In the subsequent years your monthly basic salary will increase by Rs.300. So, in the second year your salary will be Rs. 11050, in the third year it will be Rs.11350, in the fourth year it will be Rs.11650 and so on. Your perks are based on your basic salary. What will be the total basic salary in the first year, second year etc? Will they form an AP? What is the common difference?

i) Find the 9th term of the AP 23, 38, 53,..

ii) Suppose you borrow Rs.4000 from your friend. You give Rs.300 in the first month and pay Rs.200 in the subsequent months. How much of the loan you would have paid off after 8 months?

Suppose you are offered a job in the scale of 4500-125-7000.After how many years will your basic pay be 7000?

Suppose you have a job in the pay scale 4500-125-7000 and you decide to save 15% of your basic pay every month.How much will you save in 12 years?

Find the sum of the following APs :

i)19,27,....131

ii)17,31,...241

Find the sum of the first 12 terms of the following APs :

i)1 2/5,4,6 3/5....

ii)1000,4993/5,4986/5,.....

The 2 nd and 5 th terms of a GP are 10 and 1250. Find the first term and the common ratio of the GP

The 3rd and 6th terms of a GP are 18 and 486. Find the first term and the common ratio of the GP. 

Find the sum of the following GPs

i) 6 + 12 + · · · to 7 terms. 

ii) 2 + 8 + 32 + · · · + 2048 

Suppose you deposit Rs.1000 in a bank on March 31st of every year from 1995 to 1999 and you get a compound interest of 7% on your deposit. How money will the bank owe you on April 1st in 1999? 

If you deposit Rs.2000 every year on the first of March in a bank, starting from 2001, and your money earns 5% compound interest, how much will the bank owe you on 2nd of March 2006? 

Write the following sigma notation

i)1^5 + 2^5 + 3^5 + 4^5

ii)2.3+3.4+4.5+5.6+6.7

Find the sum of the following series :

i)1.3 + 2.4 +3.5+...10.12

ii)1.2.3+2.3.4+3.4.5+....9.10.11

iii)1/1.2 + 1/2.3 + 1/3.4 +...... 1/10.11