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Question
Find n if the given value of x is the nth term of the given A.P.
`1, 21/11, 31/11, 41/11,......, x = 171/11`
Solution
`1, 21/11, 31/11, 41/11`
`a_n = 171/11`
Let us take the total number terms as n
So
First term (a) = 1
Last term `(a_n) = 171/11`
Common difference (d) = `21/11 = -1`
`= (21 - 11)/11`
= 10/11
Now, as we know,
`a_n = a + (n - 1)d`
So, for the last term,
`171/11 = 1 + (n -1)(10/11)`
`171/11 = 1 + 10/11 n - 10/11`
`171/11 = (11 - 10)/11 + 10/11 n`
`171/11 = 1/11 + 10/11 n`
On further simplifying, we get,
`10/11n = 171/11 - 1/11`
`10/11 n = 170/11`
`n = ((170)(11))/((11)(10))`
n = 17
Therefore the total number of term of the given A,P is n = 17
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