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Nadusha1986 [10]
3 years ago
10

Find the first term and common difference of an AP, whose 7th term is 29/6 and 15th term is 11/2.​

Mathematics
1 answer:
777dan777 [17]3 years ago
5 0

Answer:

The first term is 13/3 and the common difference is d = 1/12

The formula is a(n) = 13/3 + (1/12)(n - 1)        

Step-by-step explanation:

The general equation for an arithmetic progression is:

a(n) = a(1) + d(n - 1), where d is the common difference/

Case 1:  n = 7:  29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)

Case 2:  n = 15:  11/2 = a(1) + d(15 - 1) =  a(1) + d(14)

Then our system of linear equations is:

a(1) + 6d = 29/6

a(1) + 14d = 11/2

Let's solve this by elimination by addition and subtraction.  Subtract the first equation from the second.  We get:

                                                             

Substituting 1/12 for d in the first equation, we get:

a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)

Then a(1) = 66/12 - 14/12 = 52/12 = 13/3

The first term is 13/3 and the common difference is d = 1/12

The arithmetic sequence formula for this problem is thus:

a(n) = 13/3 + (1/12)(n - 1)                                                                          8

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One fifth of the sum of two angles is 24 and half their difference is 14.Calculate the two angles
Brums [2.3K]
Let, the angles = a, b
It is given that, a+b /5 = 24
a + b = 120   --- equation (1)

a-b/2 = 14
a - b = 28  ---- equation (2)
a = 28 + b

Now, substitute this value of b in equation (1), 
28 + b + b = 120
2b = 120 - 28
b = 92/2
b = 46
Now, a = 28 + b = 28 + 46 = 74

In short, Your Angles are 74 and 46

Hope this helps!
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