If Sn =(3n2+2n) , find the first term and the common difference of the AP - Maths - Arithmetic Progressions

Question

If Sn =(3n2+2n) , find the first term and
the common difference of the AP

Vimala · Accepted Answer

Consider the expression $S_{n} = 3 n^{2} + 2 n$

Let $a_{1}, a_{2}, a_{3}, ... a_{n}$ be the terms of the A.P.

Now plug in the values n =1, 2, 3, ...in the given expression.

Thus,

$S_{1} = 3 + 2 = 5 S_{2} = 12 + 4 = 16 S_{3} = 27 + 6 = 33 ......$

For an A.P., $S_{1} = a_{1} = 5$

$S_{2} = a_{1} + a_{2} 16 = 5 + a_{2} 11 = a_{2}$

$a_{2} = a_{1} + d 11 = 5 + d d = 11 - 5 d = 6$

Thus, initial term of the A.P. is 5 and the common difference is 6.

If Sn =(3n2+2n) , find the first term and the common difference of the AP.