Advertisements
Advertisements
प्रश्न
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Advertisements
उत्तर
t11 = 16 and t21 = 29
t1 = ?, d = ? and t34 = ?
tn = a + (n - 1) d
t11 = a + (11 - 1) d
16 = a + 10 d ......(1)
t21 = a + (21 - 1) d
29 = a + 20d .........(2)
Subtracting equation (1) and (2)
a + 20 d = 29
a + 10 d = 16
_________________
10 d = 13
d = `13/10`
d = 1.3
Substituting d = 1.3 in equation (1)
16 = a + 10 d
a + 10 (1.3) = 16
a + 13 = 16
a = 16 - 13
a = 3
t34 = 3 + (34 - 1) (1.3)
= 3 + 33(1.3)
= 3 + 42.9
t34 = 45.9
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum given below:
34 + 32 + 30 + ... + 10
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
Which term of AP 72,68,64,60,… is 0?
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Which term of the AP 21, 18, 15, … is zero?
The sum of the first n terms of an AP in `((5n^2)/2 + (3n)/2)`.Find its nth term and the 20th term of this AP.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
Find the sum of natural numbers between 1 to 140, which are divisible by 4.
Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136
Here d = 4, therefore this sequence is an A.P.
a = 4, d = 4, tn = 136, Sn = ?
tn = a + (n – 1)d
`square` = 4 + (n – 1) × 4
`square` = (n – 1) × 4
n = `square`
Now,
Sn = `"n"/2["a" + "t"_"n"]`
Sn = 17 × `square`
Sn = `square`
Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
