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Eddi Din [679]
4 years ago
14

Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term

Mathematics
1 answer:
UNO [17]4 years ago
6 0

Answer:

The first term is -6 and common difference is 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

Tn = a + (n-1)d

T3 = a+2d

T4 = a + 3d

If the third term of an arithmetic sequence less than the fourth term by three

T3 = T4 - 3

a+2d = a+3d - 3

2d - 3d = -3

-d  = -3

d = 3

Similarly;

T7 = a+6d

T5 = a+4d

If the seventh term  is two times the fifth term, the;

T7 = 2T5

a+6d = 2(a+4d)

a+6d = 2a+8d

Since d = 3

a + 6(3) = 2a + 8(3)

a+18 = 2a + 24

a-2a = 24 - 18

-a = 6

a = -6

Hence the first term is -6 and common difference is 3

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4 years ago
- 4/7 divided by 1 3/4
GarryVolchara [31]

Answer:

0.32653061224

Step-by-step explanation:

To write 0.32653061224 as a fraction you have to write 0.32653061224 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.32653061224 = 0.32653061224/1 = 3.2653061224/10 = 32.653061224/100 = 326.53061224/1000 = 3265.3061224/10000 = 32653.061224/100000 = 326530.61224/1000000 = 3265306.1224/10000000 = 32653061.224/100000000 = 326530612.24/1000000000 = 3265306122.4/10000000000 = 32653061224/100000000000

And finally we have:

0.32653061224 as a fraction equals 32653061224/100000000000

5 0
3 years ago
Christopher walks 5km south then walks on a bearing of 036º until he is due east of his starting point. How far is he from his s
harina [27]

Christopher's distance from his starting point is 3.6 km

Since Christopher initially walks South 5 km and then walks on a bearing of of 036º until he is due east of his starting point, His distance South, his distance from his starting point and his distance from his 036º bearing, all form a right-angled triangle with opposite side to the angle 036º, as his distance from his starting point, x and the adjacent side to the angle 036º, as his distance 5 km south.

Since we have both the opposite and adjacent sides of a right-angled triangle,

From trigonometric ratios,

tanФ = opposite/adjacent

tanФ = x/5 km

Now Ф = 036º

So, tan36º = x/5km

x = 5 km(tan36º)

x = 5 km (0.7265)

x = 3.633 km

x ≅ 3.6 km to 1 decimal place.

So, Christopher's distance from his starting point is 3.6 km.

Learn more about bearing here:

brainly.com/question/11684993

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3 years ago
The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 1
nataly862011 [7]

Recall that in statistics, the mode is the value that appears most frequently in a set of data. You may find it useful to represent the data in statistical graphs such as dot plots or bar charts. In this case, we will use the following chart

As we can see from the image, The most frequently used numbers are 19 and 21. We are dealing with a bimodal data set. The mode is given by 19 and 21.

8 0
2 years ago
Monster Mike's truck decelerates from 72 m/s to 0 m/s in 6 seconds. What is his rate of deceleration?
mel-nik [20]

Answer:

this may be wrond but I think it is -12 m/s

Step-by-step explanation:

72/6=12

5 0
3 years ago
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