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fomenos
3 years ago
10

The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

Mathematics
1 answer:
Ainat [17]3 years ago
7 0

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30

       5(2a  + 4d )d           = 60

       10a    + 20d             = 60

reduce to lowest term to easy calculation by dividing through by 10

                      a + 2d       = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉  = ⁹/₂(2a + 8d )   = 69

        9(2a  + 8d )    = 30 + 69

            18a + 72d   = 99 x 2

            18a + 72d   = 198

divide through by 18 to reduce to lowest time

                a  + 4d    = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

                 a + 2d = 6

                 a + 4d = 11

                     -2d  = -5

                          d = ⁵/₂.

Now substitute  for d to get a

               a  + 2(⁵/₂) = 6

                a + 5       = 6

                           a   = 6 - 5

                            a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

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3 years ago
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3 0
3 years ago
Read 2 more answers
29. Determine the value of x.<br> abc<br> X + 42°<br> 147°<br> 2x
suter [353]

Answer:

x=35

Step-by-step explanation:

180-147=33 (angles in a straight line)

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5 0
2 years ago
More help is appreciated:))
Lera25 [3.4K]

Step-by-step explanation:

You need to translate all the points to the right 3 and up 6

Therefore, you are going to use this formula:

(x,y) ⇾ (x + 3, y + 6)

This is the same format as the previous problem, if you have noticed.

Using this, plug in each coordinate, starting with  P (5, -1)

(5, -1) ⇾ ( 5 + 3, -1 + 6)

(5, -1) ⇾ ( 8, 5 )

P^{1} = (8, 5)

Now point Q, (0, 8)

(0, 8) ⇾ (0 + 3, 8 + 6)

(0, 8) ⇾ ( 3, 14 )

Q^{1} = (3, 14)

And last but not least, the point R, (7, 5)

(7, 5) ⇾ (7 + 3, 5 + 6)

(7, 5) ⇾ ( 10, 11 )

R^{1} = (10, 11)

Therefore, P^{1} = (8, 5), Q^{1} = (3, 14), R^{1} = (10, 11) is your answer. This is the 4th option or D.

Hope this for you to understand this a bit more! =D

6 0
3 years ago
7^8 divide by 7y =7^6 find the value of y
lisabon 2012 [21]
Answer: y = 7

Explanation:

7^8/7y = 7^6
7^7/y = 7^6
In order for 7^7 to become 7^6 you need to divide by 7

Which mean y = 7

So that:
7^7/7= 7^6
7^6 = 7^6
7 0
3 years ago
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