Advertisements
Advertisements
प्रश्न
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
उत्तर
Let the number of terms taken be n.
The given A.P. is 24, 21, 18, ................
Here, a = 24 and d = 21 – 24 = –3
`S = n/2 [2a + (n - 1)d]`
`=> 78 = n/2 [2 xx 24 + (n - 1)xx (-3)]`
`=> 78 = n/2 [48 - 3n + 3]`
`=>` 156 = n[51 – 3n]
`=>` 156 = 51n – 3n2
`=>` 3n2 – 51n + 156 = 0
`=>` n2 – 17n + 52 = 0
`=>` n2 – 13n – 4n + 52 = 0
`=>` n(n – 13) – 4(n – 13) = 0
`=>` (n – 13)(n – 4) = 0
`=>` n = 13 or n = 4
∴ Required number of terms = 4 or 13
APPEARS IN
संबंधित प्रश्न
Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ……
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
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.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
How many terms of the AP: –15, –13, –11,... are needed to make the sum –55? Explain the reason for double answer.
