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
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
In an AP Given a12 = 37, d = 3, find a and S12.
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Which term of the AP 21, 18, 15, …… is -81?
The 7th term of the an AP is -4 and its 13th term is -16. Find the AP.
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
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`
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
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?
Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.
If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a.
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
x is nth term of the given A.P. an = x find x .
Q.4
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
