Advertisements
Advertisements
प्रश्न
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
Advertisements
उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a + (n - 1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
-6, 0, 6, 12,....To 13 terms
Common difference of the A.P. (d) = `a_2 - a_1`
= 0 - (-6)
= 6
Number of terms (n) = 13
First term for the given A.P. (a) = -6
So, using the formula we get,
`S_n = 13/2 [2(-6) + (13 - 1)(6)]`
`= (13/2)[-12 + (12)(6)]`
`= (13/2)[-12 + 72]`
`= (13/2)[60]`
= 390
Therefore, the sum of first 13 terms for the given A.P. is 390
APPEARS IN
संबंधित प्रश्न
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Write an A.P. whose first term is a and common difference is d in the following.
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
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
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
First four terms of the sequence an = 2n + 3 are ______.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
Three numbers in A.P. have the sum of 30. What is its middle term?
