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प्रश्न
Find n if the given value of x is the nth term of the given A.P.
`5 1/2, 11, 16 1/2, 22, ......; x = 550`
उत्तर
In the given problem, we need to find the number of terms in an A.P
We are given,
`a_n = 550`
Let us take the total number of terms as n
So,
First term (a) = `5 1/2`
Last term (`a_n`) = 500
Common difference (d) = `11 - 5 1/2`
`= 11 - 11/2`
`= (22 - 11)/2`
`= 11/2`
Now, as we know,
`a_n = a + (n - 1)d`
So for the last term
`550 = 51/2 + (n - 1)(11/2)`
`550 = 11/2 + 11/2 n - 11/2`
`550 = 11/2 n`
`n = 550(2)/11`
On further simplifying, we get,
`n = 1100/11`
n = 100
Therefore, the total number of terms of the given A.P. is `n = 100`
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