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.
Advertisements
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 of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given d = 5, S9 = 75, find a and a9.
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
How many two-digits numbers are divisible by 3?
How many three-digit numbers are divisible by 9?
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
If the common differences of an A.P. is 3, then a20 − a15 is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
The sum of all two digit odd numbers is ______.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Find the sum:
`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
