Advertisements
Advertisements
प्रश्न
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Advertisements
उत्तर
We have given a3 = 16
a + (3 − 1)d = 16
a + 2d = 16(1)
a7 − a5 = 12
[a + (7 − 1)d] − [a + (5 − 1)d] = 12
(a + 6d) − (a + 4d) = 12
2d = 12
d = 6
From equation (1), we obtain
a + 2(6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be 4, 10, 16, 22, ...
APPEARS IN
संबंधित प्रश्न
In an AP Given a12 = 37, d = 3, find a and S12.
If 12th term of an A.P. is –13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum 2 + 4 + 6 ... + 200
Find the sum:
25 + 28 + 31 + ... + 100
Is –150 a term of the AP 11, 8, 5, 2, ...?
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
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.
HINT: Let these terms be (a – d), a, (a + d).
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Simplify `sqrt(50)`
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
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
If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
First four terms of the sequence an = 2n + 3 are ______.
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
In an A.P., if Sn = n(4n + 1), find the A.P.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
