SOLUTION: 5. Find ‘a’ and ‘d’ of an A. P., if S11 = 5580, a11 = 360. [ Ans: a = 0, d = 12 ] My Answer is coming in decimals... Pls let me way out... It is a Arithmetic Progression que

Algebra ->  Test  -> Lessons -> SOLUTION: 5. Find ‘a’ and ‘d’ of an A. P., if S11 = 5580, a11 = 360. [ Ans: a = 0, d = 12 ] My Answer is coming in decimals... Pls let me way out... It is a Arithmetic Progression que      Log On


   

Question 1011604: 5. Find ‘a’ and ‘d’ of an A. P., if S11 = 5580, a11 = 360. [ Ans: a = 0, d = 12 ]

My Answer is coming in decimals...
Pls let me way out...
It is a Arithmetic Progression question
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
this answer a+=+0, d+=+12 is incorrect
to find nth term in an arithmetic sequence you use this formula:
a%5Bn%5D+=+a+%2B+%28n+-+1%29d
and to find the sum of n terms in an arithmetic sequence you use this formula:
S%5Bn%5D=%28n%2F2%29%282a%2B%28n-1%29d%29

you are given S%5B11%5D+=+5580 (sum of 11 terms),and a%5B11%5D+=+360 (11th term
360+=+a+%2B+%2811+-+1%29d
360+=+a+%2B+10d
a=360-10d........eq.1

S%5Bn%5D=%28n%2F2%29%282a%2B%28n-1%29d%29
5580=%2811%2F2%29%282a%2B%2811-1%29d%29
5580=%2811%2F2%29%282a%2B10d%29
5580=%2811%2Fcross%282%291%29%28cross%282%29a%2Bcross%2810%295d%29
5580=11%28a%2B5d%29
5580%2F11=a%2B5d
a=5580%2F11-5d.....eq.2

from eq.1 and eq.2 we have
5580%2F11-5d=360-10d.........solve for d
10d-5d=360-5580%2F11
5d=%28360%2A11%29%2F11-5580%2F11
5d=3960%2F11-5580%2F11
5d=-1620%2F11
d=-1620%2F%285%2A11%29
d=-cross%281620%29324%2F%28cross%285%29%2A11%29
highlight%28d=-324%2F11%29
then a will be
a=360-10%28-324%2F11%29........eq.1
a=360%2B3240%2F11
a=3960%2F11%2B3240%2F11
highlight%28a=7200%2F11%29


check 11th term:
a%5Bn%5D+=+a+%2B+%28n+-+1%29d if a%5B11%5D=360,a=7200%2F11 and d=-324%2F11
360+=+7200%2F11+%2B+%2811-+1%29%28-324%2F11%29
360+=+7200%2F11+%2B+10%28-324%2F11%29
360+=+7200%2F11-3240%2F11
360+=+3960%2F11
360+=+360 which confirms our solution
and
S%5Bn%5D=%28n%2F2%29%282a%2B%28n-1%29d%29 if S%5B11%5D=5580,a=7200%2F11 and d=-324%2F11
5580=%2811%2F2%29%282%287200%2F11%29%2B%2811-1%29%28-324%2F11%29%29
5580=%2811%2F2%29%2814400%2F11%2B10%28-324%2F11%29%29
5580=%2811%2F2%29%2814400%2F11-3240%2F11%29
5580=%2811%2F2%29%2811160%2F11%29
5580=%28cross%2811%291%2F2%29%2811160%2Fcross%2811%291%29
5580=%281%2F2%2911160
5580=11160%2F2
5580=5580 which confirms our solution