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प्रश्न
State whether the following sequence is an Arithmetic Progression or not:
3, 6, 12, 24,......
उत्तर
3, 6, 12, 24....
Let , 'a' be the first term of the given sequence and 'd' be the common difference.
Also, t2 , t3 , t4 be the 2nd ,3rd ,4th terms respectively.
Consider,
t2 - a = 6 - 3 = 3
t3 - t2 = 12 - 6 = 6
Here, we can see that difference between two successive terms is not constant. Hence, it is not an Arithmetic Progression
संबंधित प्रश्न
The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
If the seventh term of an AP is 1/9 and its ninth term is 1/7, find its 63rd term.
If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n)
If pth , qth and rth terms of an A.P. are a, b, c respectively, then show that
(i) a (q – r) + b(r – p) + c(p – q) = 0
(ii) (a – b) r + (b –¬ c) p + (c – a) q = 0
Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then find the middle terms
Write first four terms of the A.P. when the first term a and the common differenced are given as follows:
a = -2, d = 0
For the following arithmetic progressions write the first term a and the common difference d:
`1/5, 3/5, 5/5, 7/5`
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
0, −4, −8, −12, ...
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
−225, −425, −625, −825, ...
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their l000th terms?
Find the common difference of the A.P. and write the next two terms 51, 59, 67, 75, ..
Write the 25th term of an A.P. 12,16,20,24, .......
First term a and common difference d are given below. Find the corresponding A.P.
a = `3/4`, d = `1/2`
Two A.P.’s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. Show that the difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms.
Choose the correct alternative answer for the following sub question
1, 4, 7, 10, 13, ... Next two terms of this A.P. are ______
Decide whether the given sequence 2, 4, 6, 8,… is an A.P.
In an A.P., a = 10 and d = −3 then find its first four terms
In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.
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?
