The first term of A.P. of 20th terms is 2and its last term is 59 . Find its 6th term from the end .
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To find the 6th term from the end of an arithmetic progression (A.P.), we first need to find the common difference (d) of the A.P.
Given:
First term (a) = 2
Last term (l) = 59
Number of terms (n) = 20
We can use the formula to find the sum of an A.P.:
Sn = (n/2)(a + l)
Plugging in the values, we get:
20/2(2 + 59) = 10(61) = 610
Since we know the value of Sn, we can find the common difference (d) using the sum of A.P. formula:
Sn = (n/2)(2a + (n-1)d)
Plugging in the values, we get:
610 = (20/2)(2 + 19d)
Simplifying the equation, we have:
610 = 10(2 + 19d)
61 = 2 + 19d
59 = 19d
d = 3
Now that we know the common difference (d), we can find the 6th term from the end. Since we know the last term is 59, we can find the second-last term by subtracting the common difference (d) from the last term:
Second-last term = l - d = 59 - 3 = 56
Using the same logic, we can find the third-last term, fourth-last term, fifth-last term, and finally, the 6th term from the end:
Third-last term = second-last term - d = 56 - 3 = 53
Fourth-last term = third-last term - d = 53 - 3 = 50
Fifth-last term = fourth-last term - d = 50 - 3 = 47
Sixth-last term = fifth-last term - d = 47 - 3 = 44
Therefore, the 6th term from the end of the arithmetic progression is 44.