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प्रश्न
How many terms are there in an A.P. whose first and fifth terms are – 14 and 2, respectively and the last term is 62?
उत्तर
a = –14, a5 = 2, an= 62
a5 = a + (5 – 1)d ...[∵ an = a + (n – 1)d]
`\implies` 2 = –14 + 4d
`\implies` 4d = 16
`\implies` d = 4
Now, an = 62
`\implies` a + (n – 1)d = 62
`\implies` –14 + (n – 1)4 = 62 ...(∵ a = –14, d = 4)
`\implies` (n – 1)4 = 76
`\implies` n – 1 = `76/4` = 19
`\implies` n = 19 + 1 = 20
∴ There are 20 terms in an A.P.
संबंधित प्रश्न
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Write the first five terms of the following sequences whose nth terms are:
an = (−1)n, 2n
How many numbers of two digit are divisible by 3?
The 17th term of an A.P. is 5 more than twice its 8th term. If the 11th term of the A.P. is 43, find the nth term.
Which term of the A.P. −4, −1, 2, ... is 101?
The common difference of the AP … -4, -2, 0, 2, …. is ______.
If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be ______.
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| ______ | -3 | 18 | -5 |
How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?
