Advertisements
Advertisements
प्रश्न
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Advertisements
उत्तर
It is given that,
t9 = 0
Now,
tn = a + (n - 1)d
t9 = a + (9 - 1)d
⇒ 0 = a + 8d
⇒ a = -8d ...(1)
t29 = a + (29 - 1)d
= -8d + 28d
= 20d ...(2)
t19 = a + (19 - 1)d
= -8d + 18d
= 10d ...(3)
From (2) and (3), we get
t29 = 2t19
Hence, the 29th term is twice the 19th term.
APPEARS IN
संबंधित प्रश्न
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
The 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94. Find the common difference of the AP.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
If Sn denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
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
Q.1
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Sum of 1 to n natural number is 45, then find the value of n.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
