Question

find the number of terms of an ap 1,4,7 whose sum is 51​

Answer 1

Answer:

let the number of terms is n

here 1st term a=1

common difference d=4-1=3

so,51=n/2{2a+(n-1).d}

=> 51=n/2{2.1+(n-1).3}

=> 51=n/2{2+3n-3}

=> 51.2=n(3n-1)

=> 102=3n^2-n

=> 3n^2-n-102=0

=> 3n^2-18n+17n-102=0

=> 3n(n-6)+17(n-6)=0

=> (n-6)(3n+17)=0

here n is not -ve

so , n-6=0

n=6

number of term is 6