Advertisements
Advertisements
प्रश्न
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Advertisements
उत्तर
Since (n – 2), (4n – 1) and (5n + 2) are in A.P., we have
(4n – 1) – (n – 2) = (5n + 2) – (4n – 1)
`\implies` 4n – 1 – n + 2 = 5n + 2 – 4n + 1
`\implies` 3n + 1 = n + 3
`\implies` 2n = 2
`\implies` n = 1
∴ (n – 2), (4n – 1) and (5n + 2)
∴ (1 – 2), (4(1) – 1) and (5(1) + 2)
So, the given numbers are –1, 3, 7
`\implies` a = –1 and d = 3 – (–1) = 4
Hence, the next two terms are (7 + 4) and (7 + 2 × 4)
i.e 11 and 15
APPEARS IN
संबंधित प्रश्न
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
A sum of ₹ 2800 is to be used to award four prizes. If each prize after the first is ₹ 200 less than the preceding prize, find the value of each of the prizes.
Find the sum of the following APs:
2, 7, 12, 17, ... to 19 terms.
Write the value of a30 – a10 for the A.P. 4, 9, 14, 19,....
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Find the sum of numbers between 1 to 140, divisible by 4.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
