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प्रश्न
Which of the following form an AP? Justify your answer.
`sqrt(3), sqrt(12), sqrt(27), sqrt(48)`
उत्तर
We have,
a1 = `sqrt(3)`, a2 = `sqrt(12)`, a3 = `sqrt(27)` and a4 = `sqrt(48)`
a2 – a1 = `sqrt(12) - sqrt(3)`
= `2sqrt(3) - sqrt(3)`
= `sqrt(3)`
a3 – a2 = `sqrt(27) - sqrt(12)`
= `3sqrt(3) - 2sqrt(3)`
= `sqrt(3)`
a4 – a3 = `sqrt(48) - sqrt(27)`
= `4sqrt(3) - 3sqrt(3)`
= `sqrt(3)`
Clearly, the difference of successive terms is same
Therefore given list of numbers from an AP.
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संबंधित प्रश्न
State whether the following sequence is an AP or not: 1, 3, 6, 10………
If m times mth term of an A.P. is equal to n times its nth term, show that the (m + n) term of the A.P. is zero
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
0, -4, -8, -12, …
Write the sequence with nth term an = 5 + 2n
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.
Decide whether the given sequence 2, 4, 6, 8,… is an A.P.
In an A.P. t10 = 57 and t15 = 87, then find t21
Verify that the following is an AP, and then write its next three terms.
`sqrt(3), 2sqrt(3), 3sqrt(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?
