Advertisements
Advertisements
Question
Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.
Solution
Let 0 be the nth term of given AP i.e., an = 0
Given that, first term a = 31
Common difference, d = 28 – 31 = – 3
The nth terms of an AP, is
an = a + (n – 1)d
⇒ 0 = 31 + (n – 1)(– 3)
⇒ 3(n – 1) = 31
⇒ n – 1 = `31/3`
∴ n = `31/3 + 1`
= `34/3`
= `11 1/3`
Since, n should be positive integer.
So, 0 is not a term of the given AP.
APPEARS IN
RELATED QUESTIONS
In the following APs find the missing term in the box:
`square, 13, square, 3`
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
Write the first five terms of the following sequences whose nth terms are:
`a_n = 3^n`
Find the indicated terms in the following sequences whose nth terms are:
an = 5n - 4; a12 and a15
Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
(iv) 2, 8, 18, 32,..........
The nth term of an AP is (7 – 4n). Find its common difference.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3 (S20 − S10) ?
Which term of the AP: 27, 24, 21, ……… is zero?
In an AP, if d = –4, n = 7, an = 4, then a is ______.
Write the first three terms of the APs when a and d are as given below:
a = `1/2`, d = `-1/6`
