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प्रश्न
The first term of an A.P. is 5 and its 100th term is -292. Find the 50th term of this A.P.
उत्तर
In the given problem, we are given 1st and 100th term of an A.P.
We need to find the 50th term
Here
a = 5
`a_100 = -292`
Now, we will find d using the formula `a_n = a = (n - 1)d`
So,
Also
`a_100 = a + (100 - 1)d`
-292 = a + 99d
So to solve for d
Substituting a = 5 we get
-292 = 5 + 99d
-292 - 5 = 99d
`(-297)/99 = d`
d = -3
Thus
a = 5
d = -3
n = 50
Substituting the above values in the formula `a_n = a + (n - 1)d`
`a_50 = 5 + (50 - 1)(-3)`
`a_50 = 5 - 147`
a_50 = -142
Therefore `a_50 = -142`
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