The sum of the first 15 terms of an arithmetic sequence is 480. Find the 8th term of the sequence.

Given:

The sum of the first 15 terms of an arithmetic sequence is 480.

To find:

The 8th term of the sequence.

Solution:

We have,

We know that, the nth term of an AP is

Where, a is the first term and d is the common difference.

Putting n=8, we get the 8th term of the sequence.

The sum of first n terms is

Where, a is the first term and d is the common difference.

Divide both sides by 15.

Therefore, the 8th term of the arithmetic sequence is 32.

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

well the answer to that is xoxoxo

step-by-step explanation: