Advertisements
Advertisements
प्रश्न
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Advertisements
उत्तर
Let a be the first term and d be the common difference of the AP. Then,
`a_24 = 2a_10` (Given)
⇒ a + 23d = 2(a +9d) [an = a + (n-1) d]
⇒ a+ 23d = 2a - 18d
⇒ 2a - a = 23d -18d
⇒ a = 5d ..............(1)
Now ,
`(a_72)/(a_15) = (a+ 71d)/(a+14d) `
⇒ ` (a_72)/(a_15) = (5d + 71d)/(5d+14d)` [From(1)]
⇒ `(a_72)/(a_15) = (76d)/(19d)=4`
⇒ `a_72 = 4 xx a_15`
Hence, the 72nd term of the AP is 4 times its 15th term.
संबंधित प्रश्न
Find the sum of the odd numbers between 0 and 50.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
Find the sum of the first n natural numbers.
How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
Sum of 1 to n natural numbers is 36, then find the value of n.
If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.
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.
Write the sum of first n odd natural numbers.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
The sum of all two digit odd numbers is ______.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
