b.Find the seventeenth term of an Arithmetic Progression, whose 9th and 15th term are 19 and 37 respectively.

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Xn = a + d (n-1)

19 = a + d(8)
37 = a + d(15)
------------subtract to eliminate a

solve for d
solve for a

X17 = a + d (16)

To find the seventeenth term of an Arithmetic Progression (AP), we need to know the common difference between the terms.

For an AP, the formula to find the nth term is:
an = a1 + (n-1)d

where:
an = nth term
a1 = first term
d = common difference
n = position of the term

To find the common difference (d), we can use the given information. We are given the 9th and 15th terms as 19 and 37 respectively.

Let's use the formula to find the common difference (d):

37 = a1 + (15 - 1)d
37 = a1 + 14d

19 = a1 + (9 - 1)d
19 = a1 + 8d

Now we have a system of two equations:
37 = a1 + 14d ---- Equation 1
19 = a1 + 8d ---- Equation 2

Solving these two equations will give us the values of a1 and d, which we can then use to find the seventeenth term.

Subtracting Equation 2 from Equation 1, we get:

37 - 19 = (a1 + 14d) - (a1 + 8d)
18 = 6d
d = 3

Now we have the value of the common difference (d), which is 3.

Using Equation 1, we can find the first term (a1):

37 = a1 + 14(3)
37 = a1 + 42
a1 = -5

Now we have the first term (a1) as -5 and the common difference (d) as 3.

Finally, we can find the seventeenth term (a17) using the formula:

a17 = a1 + (17 - 1)d
a17 = -5 + (17 - 1)(3)
a17 = -5 + 16(3)
a17 = -5 + 48
a17 = 43

Therefore, the seventeenth term of the Arithmetic Progression is 43.