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The first term of an AP is 5, the last t...

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

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Let number of terms =n, first term is a = 5 and last term is l=45.
We have, `S_(n)=400`
`rArr (n)/(2)[a+l]=400 rArr (n)/(2)(5+45)=400`
`rArr n=16`
Now, `l=45` i.e., nth term = 45
`rArr a+(n-1)d=45`
`rArr 5+(16-1)d=45`
`rArr 15d=40 rArr d=(40)/(15)=(8)/(3)`
Hence , number of terms = 16 and common difference `=(8)/(3)`
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