Question

Find the lowest number in an ap such that the sum of all the terms is 105 and greatest term is 6 times the least

Answer 1

Let the least term be a, total terms be x

An=a+(n-1)d

6a=a+(n-1)d

5a=(n-1)d

n=(5a/d)+1

Sn=n/2(A+An)

105=(((5a/d)+1)/2)(a+6a)

105×2d=(5a+d)(7a)

210d= 35a²+7ad

35a²+7ad-210d=0