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प्रश्न
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
The number of bacteria in a certain food item after each second, when they double in every second.
उत्तर
Let the number of bacteria in a certain food = x
Since, they double in every second.
∴ x, 2x, 2(2x), 2(2 . 2 . x),...
i.e., x, 2x, 4x, 8x,...
Now, let t1 = x, t2 = 2x, t3 – 4x and t4 = 8x
t2 – t1 = 2x – x = x
t3 – t2 = 4x – 2x = 2x
t4 – t3 = 8x – 4x = 4x
Since, the difference between each successive term is not same.
So, the list does form an AP.
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संबंधित प्रश्न
The first three terms of an AP respectively are 3y – 1, 3y + 5 and 5y + 1. Then y equals:
(A) –3
(B) 4
(C) 5
(D) 2
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
3, 3, 3, 3, .....
Find n if the given value of x is the nth term of the given A.P.
`1, 21/11, 31/11, 41/11,......, x = 171/11`
If 3 + k, 18 – k, 5k + 1 are in A.P. then find k
For an A.P., t4 = 12 and its common difference d = – 10, then find tn
Find 27th and nth term of given A.P. 5, 2, – 1, – 4, ......
Verify that the following is an AP, and then write its next three terms.
`sqrt(3), 2sqrt(3), 3sqrt(3),...`
Write second and third term of an A.P. whose first term is 6 and common difference is – 3.
The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
- If the first circular row has 30 seats, how many seats will be there in the 10th row?
- For 1500 seats in the auditorium, how many rows need to be there?
OR
If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after the 10th row? - If there were 17 rows in the auditorium, how many seats will be there in the middle row?
