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प्रश्न
Find the number of terms in the following A.P.: 7, 13, 19, ..., 205.
How many terms are there in the A.P.?
7, 13, 19, ..., 205.
उत्तर
For this A.P.,
a = 7
d = a2 − a1 = 13 − 7 = 6
Let there are n terms in this A.P.
an = 205
We know that
an = a + (n - 1) (d)
⇒ 205 = 7 + (n - 1) (6)
⇒ 205 = 7 + 6n - 6
⇒ 6n = 205 + 6 - 7
⇒ 6n = 204
⇒ n = `204/6`
⇒ n = 34
Thus, the required number of terms is 34.
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