Advertisements
Advertisements
प्रश्न
उत्तर
The given sequence is 2, 4, 6, 8 ... 344, 346, 348
Now, surely the above-mentioned range is in an A.P. or Arithmetic Progression. (Because the difference between two consecutive numbers in the given series is always constant.)
The above sequence is an A.P. with
a = t1 = 2,
d = t2 - t1 = 4 - 2 = 2,
tn = 348
Since tn = a + (n - 1) d
∴ 348 = 2 + (n - 1) 2
∴ 348 = 2 - 2n + 2
∴ 348 = 2 + 2n - 2
∴ 348 = 2n
∴ n = `348/2` = 174
∴ n = 174
Thus, the number of terms (n) = 174.
Now, Sn = `n/2` [2a + (n - 1)d]
∴ S174 = `174/2` [2(2) + (174 - 1)2]
= 87 [4 + (173)2]
= 87 [4 + 346]
= 87 × 350
= 30450
Hence, the sum of all even numbers between 1 and 350 is 30450.
संबंधित 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.
In an AP Given a12 = 37, d = 3, find a and S12.
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
Find the middle term of the AP 6, 13, 20, …., 216.
In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) 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
The sum of first n odd natural numbers is ______.
Q.2
Q.20
In an A.P. a = 2 and d = 3, then find S12
Find the sum of all odd numbers between 351 and 373.
