Advertisements
Advertisements
प्रश्न
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
Advertisements
उत्तर
It is given that (3k -2) ,(4k -6) and (k +2) are three consecutive terms of an AP.
∴ (4k - 6) - (3k - 2) = (k+2) - (4k - 6)
⇒ 4k - 6 - 3k + 2 = k+2 - 4k +6
⇒ k - 4 = -3k + 8
⇒ k+ 3k = 8+4
⇒ 4k = 12
⇒ k = 3
Hence, the value of k is 3.
APPEARS IN
संबंधित प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
If (2p – 1), 7, 3p are in AP, find the value of p.
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
The sum of first n odd natural numbers is ______.
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Q.6
Write the formula of the sum of first n terms for an A.P.
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
