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प्रश्न
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
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उत्तर
Yes.
Let the first term, common difference and the number of terms of an AP are a, d and n respectively.
Let the nth term of an AP be 55
i.e., Tn = 55
We know that,
The nth term of an AP,
Tn = a + (n – 1)d ...(i)
Given that,
First term (a) = 7
and common difference (d) = 10 – 7 = 3
From equation (i),
55 = 7 + (n – 1) × 3
⇒ 55 = 7 + 3n – 3
⇒ 55 = 4 + 3n
⇒ 3n = 51
∴ n = 17
Since, n is a positive integer.
So, 55 is a term of the AP.
Since, n = 17
Therefore, 17th term of an AP is 55.
संबंधित प्रश्न
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]
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