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.
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
The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
How many terms of the AP `20, 19 1/3 , 18 2/3, ...` must be taken so that their sum is 300? Explain the double answer.
Find the sum of all multiples of 9 lying between 300 and 700.
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
