Advertisements
Advertisements
Question
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
Solution
Let a be the first term and d be the common difference of the AP. Then,
`10 xx a_10 = 15 xx a_15 ` (Given)
⇒10(a +9d) = 15 (a+14d) { an = a+ (n-1)d]
⇒ 2 (a + 9d)=(a +14d)
⇒ 2a + 18d = 3a + 42d
⇒ a= -24d
⇒a + 24d = 0
⇒ a+ (25-1) d=0
⇒ a25 =0
Hence, the 25th term of the AP is 0.
APPEARS IN
RELATED QUESTIONS
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
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 =
The sum of first 20 odd natural numbers is
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
In an AP, if Sn = n(4n + 1), find the AP.
