Sum of the First 'N' Terms of an Geometric Progression

A survey was conducted in Aadarsh Vidyalaya to know the inclication of students towards different subjects. The data obtained is presented by the adjacent pie diagram. If the total number of students was 500, answer the following questions. 

(i) How many students show inclination towards mathematics ? 

(ii) How many students are inclined towards social sciences ? 

(iii) How many more students are inclined towards languages than
science ?  

Sachin invested in a national saving certificate scheme. In the first year he invested Rs 5000 , in the second year Rs 7000, in the third year Rs 9000 and so on. Find the total amount that he invested in 12 years.

Sachin invested some amounts in National Saving Certificates in a specific way. In the first year, he invested  4,000 in the second year  6,000 in the third year  8,000 and so on for  12 years. Find the total amount he invested in 12 years. 

The 11^th term and the 21^st term of an A.P. are 16 and 29 respectively, then find the 41^th term of that A.P.

A man borrows Rs 8000 and agrees to repay with a total interest of Rs 1360 in 12 monthly installments. Each installment being less than the preceding one by Rs 40. Find the amount of the first and last installments.

The first term and the common difference of an A.P. is 10 and 5 respectively. Complete the following activity to find the sum of first 30 terms of the A. P.  

`S_n=n/2[ ____+(n-1)d ]`

`∴ s_30=30/2[20+(30-1)xx _____ ]`

=`15[20+________]`

=`15xx165`

=_________