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प्रश्न
Show that the sequence defined by an = 3n2 − 5 is not an A.P
उत्तर
In the given problem, we need to show that the given sequence is not an A.P
Here,
an = 3n2 − 5
Now, first, we will find its few terms by substituting n = 1, 2, 3,4,5
so
Substituting n = 1, we get
`a_1 = 3(1)^2 - 5`
`a_1 = -2`
Substituting n = 2, we get
`a_2 = 3(2)^2 - 5`
`a_2 = 7`
Substituting n = 3, we get
`a_3 = 3(3)^2 - 5`
`a_3 = 22`
Substituting n = 4, we get
`a_4 = 3(5)^2 - 5`
`a_4 = 43`
Substituting n = 5, we get
`a_5 = 3(5)^2 - 5`
`a_5 = 70`
Further, for the given sequence to be an A.P,
We find the common difference (d) = `a_2 - a_1 - a_3 - a_2`
Thus
`a_2 - a_1 = 7 - (-2)`
= 9
Also
`a_3 - a_2 = 22 -7`
= 15
So,`a_2 - a_1 != a_3 - a_2`
Hence, the given sequence is not an A.P.
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| Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasure. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize. While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the nth spot is 20 + 4n, then answer the following questions to help the players in spotting the clues: |
- Which number is on first spot? 1
- Which spot is numbered as 112? 2
OR - What is the sum of all the numbers on the first 10 spots? 2
- Which spot is numbered as 112? 2
- Which number is on the (n – 2)th spot? 1
