Advertisements
Advertisements
प्रश्न
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, Which term of it is zero?
उत्तर
Given that,
a3 = 4
a9 = −8
We know that,
an = a + (n − 1) d
a3 = a + (3 − 1) d
4 = a + 2d ...(I)
a9 = a + (9 − 1) d
−8 = a + 8d ...(II)
On subtracting equation (I) from (II), we obtain
−12 = 6d
d = −2
From equation (I), we obtain
4 = a + 2 (−2)
4 = a − 4
a = 8
Let nth term of this A.P. be zero.
an = a + (n − 1) d
0 = 8 + (n − 1) (−2)
0 = 8 − 2n + 2
2n = 10
n = 5
Hence, 5th term of this A.P. is 0.
संबंधित प्रश्न
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP given an = 4, d = 2, Sn = −14, find n and a.
Find the sum of first 15 multiples of 8.
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum 25 + 28 + 31 + ….. + 100
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3,..., 4 1/3.`
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.
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
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Q.6
Q.2
Q.13
Q.17
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
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 sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.
If a = 6 and d = 10, then find S10
First four terms of the sequence an = 2n + 3 are ______.
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
