The following is an A.P 9,x,y,z,25 find (a)the values of x,y,z (b)60 term
The full workings
In an Arithmetic Progression:
an = a1 + ( n - 1 ) d
where
a1 = the initial term
d = the common difference of successive members
an = the nth term
In your A.P:
9 , x , y , z , 25
a1 = 9
a5 = a1 + 4 d = 9 + 4 d = 25
4 d = 25 - 9
4 d = 16
d = 16 / 4
d = 4
Now:
x = a2 = a1 + d = 9 + 4 = 13
y = a3 = a1 + 2 d = 9 + 2 ∙ 4 = 9 + 8 = 17
z = a4 = a1 + 3 d = 9 + 3 ∙ 4 = 9 + 12 = 21
a60 = a1 + 59 d
a60 = 9 + 59 ∙ 4 = 9 + 236 = 245
This answer is correct because i have cross-chack my textbook.
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The answer is on the way but I compuse too. I need more explanation please.
245
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To find the values of x, y, and z in the arithmetic progression (AP) 9, x, y, z, 25 and the 60th term, you can use the formulas for arithmetic progressions.
(a) Finding the values of x, y, and z:
In an arithmetic progression, the difference between consecutive terms is constant. We can find this common difference using the known terms in the sequence.
Given:
First term (a) = 9
Fourth term (a + 3d) = 25
Using the formula for the nth term of an arithmetic progression:
a_n = a + (n-1)d
Let's use the fourth term, a + 3d = 25:
9 + 3d = 25
Solving for d, the common difference:
3d = 25 - 9
3d = 16
d = 16/3
Now we can find the values of x, y, and z using the common difference:
x = a + d
y = a + 2d
z = a + 3d
x = 9 + (16/3)
y = 9 + 2(16/3)
z = 9 + 3(16/3)
(b) Finding the 60th term:
To find the 60th term, we can use the formula mentioned earlier:
a_n = a + (n-1)d
Substituting the known values:
a_60 = 9 + (60-1)(16/3)
Simplifying the equation gives you the 60th term of the arithmetic progression.
Using these formulas, you can find the desired values and terms in the given AP.