Advertisements
Advertisements
Question
Is -150 a term of the AP 11, 8, 5, 2, ……?
Advertisements
Solution
The given AP is 11, 8, 5, 2, ……
Here, a= 11and d = 8 - 11 = - 3
Let the nth term of the given AP be - 150. Then,
an = -150
⇒ 11+ (n-1) × (-3) = - 150 [ an = a + (n-1) d]
⇒ -3n +14 = -150
⇒ -3n = -164
⇒ n= `164/3 = 54 2/3`
But, the number of terms cannot be a fraction.
Hence, -150 is not a term of the given AP.
APPEARS IN
RELATED QUESTIONS
In an AP, given a = 7, a13 = 35, find d and S13.
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the sum 25 + 28 + 31 + ….. + 100
Is 184 a term of the AP 3, 7, 11, 15, ….?
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
The first term of an AP is p and its common difference is q. Find its 10th term.
If the sum of first p terms of an AP is 2 (ap2 + bp), find its common difference.
If the common differences of an A.P. is 3, then a20 − a15 is
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Q.6
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.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
Write the formula of the sum of first n terms for an A.P.
For an A.P., if t1 = 1 and tn = 149, then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `n/2 (square + square)`
= `n/2 xx square`
= `square` n, where n = 75
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Find the sum of all even numbers from 1 to 250.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
