Find, 100 is a term of the A.P.25,31,.........or not.
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Given AP: 25, 31....
a = 25, d = 31 - 25 = 6
Let us consider an = 100
an = a + (n - 1)*d
a + (n - 1)*d = 100
25 + (n - 1)*6 = 100
(n - 1)*6 = 100 - 25
(n - 1)*6 = 75
n - 1 = 75/6
n = (75/6) + 1
n = 81/6
n = 13.5
But number of terms, n in an AP is always integer value. It can never be a fraction or decimal.
Therefore 100 cannot be a term in given AP.
a = 25, d = 31 - 25 = 6
Let us consider an = 100
an = a + (n - 1)*d
a + (n - 1)*d = 100
25 + (n - 1)*6 = 100
(n - 1)*6 = 100 - 25
(n - 1)*6 = 75
n - 1 = 75/6
n = (75/6) + 1
n = 81/6
n = 13.5
But number of terms, n in an AP is always integer value. It can never be a fraction or decimal.
Therefore 100 cannot be a term in given AP.
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