Advertisements
Advertisements
प्रश्न
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
Advertisements
उत्तर
Let a be the first term and d be the common difference of the A.P.
Then, 4 × a4 = 18 × a18 ...(Given)
⇒ 4(a + 3d) = 18(a + 17d) ...[∵ an = a + (n – 1)d]
⇒ 2(a + 3d) = 9(a + 17d)
⇒ 2a + 6d = 9a + 153d
⇒ 7a = –147d
⇒ a = –21d
⇒ a + 21d = 0
⇒ a + (22 – 1)d = 0
⇒ a22 = 0
Hence, the 22nd term of the A.P. is 0.
APPEARS IN
संबंधित प्रश्न
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Find the sum given below:
34 + 32 + 30 + ... + 10
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
How many three-digit natural numbers are divisible by 9?
The nth term of an AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Write the nth term of an A.P. the sum of whose n terms is Sn.
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
Find the sum of all even numbers from 1 to 250.
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?
