Arithmetic Series I - Challenging

Question 1: Can numbers

1, \sqrt{2}, \sqrt{3}

be the terms of an arithmetic progression?

A

Yes, anyway

B

No

C

Yes, only in the case when

a_{1} = 1

D

No, unless

a_{2} = \sqrt{2}; a_{3} = \sqrt{3}

Question 2: Find the first term and the difference of the arithmetic progression (

a_{n}

) if

a_{5} + a_{12} = 41; a_{10} + a_{14} = 62

.

A

a_{1} = - 4; d = 3

B

a_{1} = 2; d = 3

C

a_{1} = - 9.5; d = 4

D

a_{1} = - 2; d = 3

Question 3: What is the value of

x

when expressions

x^{2} - 4, 5 x + 3, 3 x + 2

in this right order form an arithmetic progression?

A

\emptyset

B

- 1; 8

C

8

only

D

- 1

only

Question 4: In which case the equation

a_{1} \times a_{4} = a_{2}^{2}

works for the terms of an arithmetic sequence?

A

Only if

a_{1} = d

B

a_{1} = d

or

d = 0

C

It cannot work

D

Only if

d = 0

Question 5: In what order should expressions

{(a + b)}^{2}, {(a - b)}^{2}, a^{2} + b^{2}

be put to form an arithmetic sequence?

A

{(a + b)}^{2}, {(a - b)}^{2}, a^{2} + b^{2}

B

Only

{(a + b)}^{2}, a^{2} + b^{2}, {(a - b)}^{2}

C

{(a - b)}^{2}, {(a + b)}^{2}, a^{2} + b^{2}

D

{(a + b)}^{2}, a^{2} + b^{2}, {(a - b)}^{2}

or

{(a - b)}^{2}, a^{2} + b^{2}, {(a + b)}^{2}

Test: Arithmetic Series I - Challenging