Advertisements
Advertisements
Question
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
Advertisements
Solution
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
RELATED QUESTIONS
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
How many multiples of 4 lie between 10 and 250?
In an AP given a3 = 15, S10 = 125, find d and a10.
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Find the sum of all 3 - digit natural numbers which are divisible by 13.
How many two-digit number are divisible by 6?
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
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?
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
Find the sum of all odd numbers between 351 and 373.
Find the sum of all 11 terms of an A.P. whose 6th term is 30.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
