JEE Main · MathematicsMedium

$If the sum of the first n terms of an arithmetic progression is given by S_{n} = 3 n^{2} + 5 n, then the common difference of the progression is:$

A. $3$
B. $5$
C. $6$
D. $8$

Show correct answer & step-by-step solution

Correct answer: C — $6$

Solution

The n^{t h} term is a_{n} = S_{n} - S_{n - 1} = (3 n^{2} + 5 n) - (3 (n - 1)^{2} + 5 (n - 1)) = 6 n + 2 . The common difference d = a_{n} - a_{n - 1} = 6 .

Attempt this question & track your score

Sign up free to answer, get instant scoring, and let SolveGini track which Mathematics topics you need to revise.

Attempt & Track Free →

More Algebra practice questions

$What is the value of the determinant of the matrix [[2, 3], [1, 4]]?$
$Find the number of ways to arrange the letters of the word CAT.$
$F in d t h e v a l u eo f x i f 2^{(} x + 3) = 32.$
$I f t h er oo t so f t h e q u a d r a t i ce q u a t i o n x^{2} - 6 x + k = 0 a r ee q u a l, f in d t h e v a l u eo f k .$
$I f t h es u m o f t h e f i r s t n t er m so f ana r i t hm e t i c p r o g r ess i o ni s g i v e nb y S n = 3 n^{2} + n, f in d t h eco mm o n d i f f er e n ceo f t h$
$T h e n u mb er o f r e a l so l u t i o n so f t h ee q u a t i o n ∣ x^{2} - 3 x + 2∣ = x - 1 i s :$
$T h e v a l u eo f t h e d e t er minan t o f a 3 x 3 ma t r i x w h er ee a c h e l e m e n t a_{i} j i s d e f in e d a s i + j i s :$
$The number of ways to arrange the letters of the word 'MATHEMATICS' such that the vowels always come together is:$
$I f a l p haan d b e t aa r e t h er oo t so f t h ee q u a t i o n x^{2} - 6 x + 2 = 0, t h e n t h e v a l u eo f a l p h a^{4} + b e t a^{4} i s :$
$I f o m e g ai s a co m pl e x c u b er oo t o f u ni t y, f in d t h e v a l u eo f (1 + o m e g a) (1 + o m e g a^{2}) (1 + o m e g a^{4}) (1 + o m e g a^{8}) .$
$F in d t h e n u mb er o f r e a l so l u t i o n s t o t h ee q u a t i o n 2^{x} + 3^{x} = 5^{x} .$
$If the roots of the equation x^3 - 3x^2 + 4x - 1 = 0 are alpha, beta, and gamma, then find the value of (alpha^2 + beta^$

View all Algebra questions →