Question

the sum of ap 34,32,30................,10 is:-

Answer 1

Given:-
a = 34 , d = - 2 , l = 10
We know that,
Sn = n/2 ( a + l)

We have to find out n =?..
An = a + ( n - 1) d
10 = 34 + ( n- 1) (- 2)
10 = 34 - 2n + 2
10 = 36 - 2n
- 26 = - 2n
n = 13.
S13 = 13/2 ( 34 + 10)
S13 = 13/2 x 44
S13 = 13 x 22
S13 = 286.
Hope it helps u.....

Answer 2

Given,

A.P. = 34, 32, 30,            ,10.

To Find,

The sum of the given A.P.

Solution,

We can solve the question using the following steps:

To find the sum of the given A.P. we can use the formula,

$S_{n} = \frac{n}{2} ( 2a + (n - 1)d)$        ----------------- (1)

Where $S_{n} =$ Sum of n terms

             $n =$ The number of terms

             $a =$ The first term

             $d =$ The common difference

In the given A.P.,

$a = 34$

To find the common difference, we will subtract any two consecutive terms.

Subtracting the first term from the second, the common difference will be:

$d = 32 - 34 = -2$

Now, to find $n$,

We know that the nth term of an A.P. is given as,

$T_{n} = a + (n - 1)d$

To find the total number of terms, we can calculate the nth value of the last term. By doing this, we can find the total number of terms in the A.P.

Using the above formula,

$T_{n} = 10, a = 34, n = ?, d = -2$

$10 = 34 + (n - 1)(-2)$

$-24 = -2n + 2$

$-26 = -2n$

$n=13$

Hence, the total number of terms is 13.

Substituting all the values in equation (1),

$S_{n} = \frac{13}{2} (2*34 + (13 - 1)(-2))$

   $= 6.5(68 + 12*(-2))$

   $= 6.5(68 - 24)$

   $= 6.5*44$

   $= 286$

Hence, the sum of the A.P. is 286.