Advertisements
Advertisements
प्रश्न
Find t21, if S41 = 4510 in an A.P.
Advertisements
उत्तर
For an A.P., let a be the first term and d be the common difference.
S41 = 4510 ...[Given]
Since `S_n = n/2 [2a + (n - 1)d]`,
`S_41 = 41/2 [2a + (41 - 1)d]`
∴ `4510 = 41/2 (2a + 40d)`
∴ `4510 = 41/2 xx 2 (a + 20d)`
∴ 4510 = 41(a + 20d)
∴ a + 20d = `4510/41`
∴ a + 20d = 110 ...(i)
Now, tn = a + (n – 1)d
∴ t21 = a + (21 – 1)d
= a + 20d
∴ t21 = 110 ...[From (i)]
APPEARS IN
संबंधित प्रश्न
Find the sum given below:
34 + 32 + 30 + ... + 10
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Find the sum of first 15 multiples of 8.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progressions:
−26, −24, −22, …. to 36 terms
Find the sum of all even integers between 101 and 999.
If k, (2k - 1) and (2k + 1) are the three successive terms of an AP, find the value of k.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
The nth term of an A.P., the sum of whose n terms is Sn, is
Q.2
Q.18
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
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`
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
