Question

In an arithmetic progression, the sum, sn, of the first n terms is given by sn = 2n2 + 8n. find the first term and the common difference of the progression.

Answer 1

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Answer 2

Given :

The sum, of the first n terms is given by $S_n$ = 2 n² + 8 n

To Find :

The first term

The common difference

Solution :

Sum of n term of an Arithmetic Progression is given as

$S_n$  = $\dfrac{n}{2}$ [2 a + ( n - 1 ) d]

For n = 1

$S_n$  = $\dfrac{1}{2}$ [2 a + ( 1 - 1 ) d]

   = $\dfrac{2a}{2}$

   = a

here

∵ $S_n$ = 2 n² + 8 n

For n = 1

$S_1$  =  2 ( 1 )² + 8 × 1

    = 2 + 8

    = 10

So, Sum of First term = 10

Again

For n = 2

$S_2$  =  2 ( 2 )² + 8 × 2

    = 8 + 16

    = 24

So, Sum of second term = 24

So, First term = $S_2$ - $S_1$

                      = 24 - 10

                      = 14

∴  The First term = a = 14

Now,

Common difference between terms = a - $S_1$

Or,                                                     d = 14 - 10

∴                                                         d = 4

So, The common difference = 4

Hence, The First term is 14

And The common difference is 4  . Answer