Sequences — Quiz 6

Questions in this quiz (6)

1. The sum of $$n$$ terms of an arithmetic progression is written as $$S_n = pn + qn^2$$. Find the common difference of the arithmetic progression.

   • $$d = 2$$
   • $$d = q$$
   • $$d = 2q$$
   • $$d = \sqrt{2q}$$

2. What is the value of $$k$$ such that $$k+1$$, $$3k-1$$,$$4k+1$$ are in arithmetic progression?

   • 7
   • 5
   • 4
   • 6

3. The houses in a row are numbered consecutively from 1 to 49. Show that there is a value of $$x$$ such that the sum of the numbers of the houses preceding the house numbered $$x$$ is equal to the sum of the numbers of the houses following it. Find the value of $$x$$.Hint: $$S_{x-1} = S_{49} - S_x$$

   • 12
   • 24
   • 25
   • 35

4. The sum of the $$5^{th}$$ and $$9^{th}$$ terms of an arithmetic progression is $$30$$, and the sum of the $$7^{th}$$ and $$11^{th}$$ terms is $$50$$. Find the first three terms of the arithmetic progression.

   • $$10, 15, 20$$
   • $$-30, -15, 0$$
   • $$-15, -10, -5$$
   • $$5, 10, 15$$

5. How many terms of the arithmetic progression: $$9, 17, 25, \ldots$$ must be taken to give a sum of $$636$$?

   • 12
   • 10
   • 8
   • 9

6. Find the arithmetic progression whose sum to n terms is $$2n^2 + n$$.

   • The arithmetic progression is $$3, 7, 11, 15, \ldots$$ with first term $$a = 3$$ and common difference $$d = 4$$.
   • The arithmetic progression is $$5, 7, 11, 13, \ldots$$ with first term $$a = 5$$ and common difference $$d = 2$$.
   • The arithmetic progression is $$3, 6, 9, 12, \ldots$$ with first term $$a = 3$$ and common difference $$d = 3$$.
   • The arithmetic progression is $$5, 8, 11, 14, \ldots$$ with first term $$a = 5$$ and common difference $$d = 3$$.