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प्रश्न
How many terms are there in the A.P.?
`-1, 5/6, 2/3, 1/2,.....10/3`
उत्तर
In the given problem, we are given an A.P.
We need to find the number of terms present in it
So here we will find the value of n using the formula, `a_n = a + (n - 1)d`
Here, A.P is `-1, 5/6, 2/3, 1/2,.....10/3`
The first term (a) = -1
The last term `(a_n) = 10/3`
Now
Common difference (d) = `a_1 - a`
`= -5/6 - (-1)`
`= -5/6 + 1``
`= (-5 + 6)/61
`= 1/6`
Thus, using the above mentioned formula, we get,
`10/3 = -1 + (n - 1) 1/6`
`10/3 +1 = 1/6 n - 1/6`
`13/3 + 1/6 = 1/6 n`
Further solving for n, we get
`(26 + 1)/6 = 1/6 n`
`n = 27/6 (6)`
n = 27
Thus n = 27
Therefore, the number of terms present in the given A.P is 27
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