Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The 10th term of the A.P. 5, 8, 11, 14, ... is
2. If the third term of a G.P. is 4, then the product of its first 5 terms is
3. The Arithmetic Mean between 4 and 16 is
4. Which term of the G.P. 2, 1, 1/2, 1/4, ... is 1/128?
5. The sum of the first $n$ natural numbers is
6. Find the sum of all natural numbers between 100 and 1000 which are multiples of 5.
7. Find the 20th term of the G.P. $5/2, 5/4, 5/8, \dots$.
8. If the sum of $n$ terms of an A.P. is $3n^2 + 5n$, find the $n^{th}$ term.
9. The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms.
10. How many terms of the A.P. 24, 21, 18, ... must be taken so that their sum is 78?
11. If $\frac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is the Arithmetic Mean between $a$ and $b$, then find the value of $n$.
12. Case Study: A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs. 5 every month.
    (i) Find the amount paid in the 30th installment.
    (ii) Find the total amount paid in 30 installments.
    (iii) If the total loan is Rs. 5175, is it cleared in 30 installments?