Advertisements
Advertisements
प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Advertisements
उत्तर
Let the first term and the common difference of the given A.P. be a and d, respectively.
Sum of the first 7 terms, S7 = 49
We know
`S = n/2[2a + (n - 1)d]`
⇒ `7/2(2a + 6d) = 49`
⇒ `7/2 xx 2(a + 3d) = 49`
⇒ a + 3d = 7 ...(1)
Sum of the first 17 terms, S17 = 289
⇒ `17/2(2a + 16d) = 289`
⇒ `17/2 xx 2(a + 8d) = 289`
⇒ a + 8d = `289/17`
⇒ a + 8d = 17 ...(2)
Subtracting (2) from (1), we get
5d = 10
d = `5/10`
⇒ d = 2
Substituting the value of d in (1), we get
a = 1
Now,
sum of the first n terms is given by
`S_n = n/2[2a + (n - 1)d]`
= `n/2[2 xx 1 + (n - 1) xx 2]`
= `n/2 [2 + 2n - 2]`
= `n/2 [2n]`
= n2
Therefore, the sum of the first n terms of the A.P. is n2.
APPEARS IN
संबंधित प्रश्न
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
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
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
If the numbers a, 9, b, 25 from an AP, find a and b.
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
Q.16
Find the sum of all members from 50 to 250 which divisible by 6 and find t13.
Find the sum of the first 10 multiples of 6.
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.
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
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 = 3n2 + 5n and ak = 164, find the value of k.
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
