Advertisements
Advertisements
Question
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
Advertisements
Solution
Let a be the first term and d be the common difference of the AP. Then,
`a_19 = 3a_6` (Given)
⇒ a + 18d = 3 (a+ 5d) [ an = a + (n-1) d]
⇒ a + 18d = 3a + 15d
⇒ 3a - a = 18d - 15d
⇒ 2a = 3d ................(1)
Also,
a9 = 19 (Given)
⇒ a +8d = 19 ..............(2)
From (1) and (2), we get
`(3d)/2 + 8d = 19`
`⇒ (3d +16d)/2 = 19`
⇒ 19d =38
⇒ d =2
Putting d = 2 in (1), we get
2a = 3 × 2=6
⇒ a = 3
So,
a2 = a + d = 3+2 = 5
a3 = a +2d = 3+2 × 2=7
Hence, the AP is 3,5,7,9,........
APPEARS IN
RELATED QUESTIONS
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
Find the sum of first 15 multiples of 8.
Find the sum of the odd numbers between 0 and 50.
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceed the second term by 6, find three terms.
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?
Which term of the AP 21, 18, 15, …… is -81?
Divide 24 in three parts such that they are in AP and their product is 440.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\] are in A.P. Then, x =
Q.16
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
