Question

Which sequences are arithmetic? Select three options.

–8.6, –5.0, –1.4, 2.2, 5.8, …

2, –2.2, 2.42, –2.662, 2.9282, …

5, 1, –3, –7, –11, …

–3, 3, 9, 15, 21, …

–6.2, –3.1, –1.55, –0.775, –0.3875, …

Answer 1

Answer:

observer the common difference

–8.6, –5.0, –1.4, 2.2, 5.8, … common difference 3.6

5, 1, –3, –7, –11, … common difference -4

–3, 3, 9, 15, 21, common difference 6

Answer 2

a), c) and d) are arithmetic sequence.

Step-by-step explanation:

Check options:

a) –8.6, – 5.0, – 1.4, 2.2, 5.8, …

Here, first term = – 8.6, second term = - 5.0 and third term = - 1.4

∴ Common difference (d) = Second term - First term = Third term - Second term

Second term - First term = – 5.0 - (– 8.6) = - 5.0 + 8. 6 = 3.6

Third term - Second term = – 1.4 - (– 5.0) = – 1.4 + 5 = 3.6

The given sequence are arithmetic sequence.

b) 2, – 2.2, 2.42, – 2.662, 2.9282, …

Here, first term = 2, second term = – 2.2 and third term = 2.42

∴ Common difference (d) = Second term - First term = Third term - Second term

Second term - First term = – 2.2 - 2= - 4.2

Third term - Second term = 2.42 - (– 2.2) = 2.42 + 2.2 = 4.62

The given sequence are not arithmetic sequence.

c) 5, 1, –3, –7, –11, …

Here, first term = 5, second term = 1 and third term = - 3

∴ Common difference (d) = Second term - First term = Third term - Second term

Second term - First term = 1 - 5= - 4

Third term - Second term = - 3 - 1 = - 4

The given sequence are arithmetic sequence.

d) – 3, 3, 9, 15, 21, …

Here, first term = - 3, second term = 3 and third term = 9

∴ Common difference (d) = Second term - First term = Third term - Second term

Second term - First term = 3 - ( - 3) = 3 + 3 = 6

Third term - Second term = 9 - 3 = 6

The given sequence are arithmetic sequence.

e) – 6.2, – 3.1, – 1.55, – 0.775, – 0.3875, …....

Here, first term = – 6.2, second term = – 3.1 and third term = – 1.55

∴ Common difference (d) = Second term - First term = Third term - Second term

Second term - First term = – 3.1 - (– 3.1) = – 3.1 + 3.1 = 0

Third term - Second term = – 1.55 - ( – 3.1) = – 1.55 + 3.1 = 1.55

The given sequence are not arithmetic sequence.