Question

Find the sum of the A.P 34+32+30--------+10
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Answer 1

Answer : 286

Step-by-step explanation:

✓ Common Difference = -2

✓ First term = 34

Number of terms is given by :

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

✓ Number of terms = 13

Now Sum is given by :

$\frac{x(34 + 10)}{2} = 22 \times x = 22 \times 13 = 286$

Answer 2

In this AP,

a =  34

d =  a2 - a1

  =  32 - 34

  =  - 2

∵

$a_{n} = a+(n-1)d\\\\10=34+(n-1) -2\\\\10=34-2n+2\\\\2n=36-10\\\\2n=26\\\\n=13$

So, the sum will be :-

$S_{n}=\frac{n}{2}[2a+(n-1)d]\\\\S_{n}=\frac{13}{2}[2*34+(13-1)*(-2)]\\\\S_{n}=\frac{13}{2}[ 68+(12)-2]\\\\S_{n}=\frac{13}{2}[68-48]\\\\S_{n}=\frac{13}{2}*20\\\\S_{n}=13*10\\\\S_{n}=130$

           Ans.

Hope it helps...