The sum of n-terms of an AP .is 56 and the common difference is 2. If first term is an integer and n>1 then n can have value. (A) 7 (B) 8 (C) 24 (D) 2
The sum of n terms of an AP is 3n^2+nand its common difference is 6,then find its first term.
Sum of nn terms of an AP Sn=n2[2a+(n−1)d]Sn=n2[2a+(n−1)d] Sn=n2[2(a−b)(a+b)+(n−1)(2a−b)(a+b)]Sn=n2[2(a−b)(a+b)+(n−1)(2a−b)(a+b)] =n2[2a−2b+2an−2a−bn+ba+b]=n2[2a−2b+2an−2a...
The formula Sn= n/2 [a + l] gives the sum of an AP’s n terms. By changing the values of ‘a’ and ‘l’ in the formula above, we get Sₙ = n/2 x [1 + (2n-1)] Sₙ = n/2 x [2n] Sₙ = n x n Sₙ = n² Therefore, when n = 1, S₁ = ...
Sum of the First n Terms of Arithmetic ProgressionThe formula for the first n terms of an arithmetic progression isFormula (First n Numbers in an AP): Sn = n/2 [ 2a + ( n – 1 ) d ] where Sn = sum of the n termsn = total termsa = first termd = common difference...
Arithmetic Progression (AP) is a sequence of numbers in order that the common difference of any two successive numbers is a constant value. Learn with arithmetic sequence formulas and solved examples.
1, 2, 3, 4,…., n this is an ap with first term a = 1 and last term l = n. we know that, the sum of n terms of ap when the first and last terms are known is given by: s = (n/2) (a + l) = (n/2)(1 + n) = n(n + 1)/2 therefore, the sum of the ...
Apéry's constant arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio, computed using quantum electrodynamics. displaystylezeta(3) is known to be an irrational number which was...
How many terms of the series∑n=1∞3(2n+1)6are needed so that the sum is accurate to within 0.00001? Limits and Series To begin, we need to determine if the series converge or not. If they converge, we know the error approximation is: ...
To find the 15th term of the arithmetic progression (A.P.) where the sum of the first n terms is given by