Question

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- find the number of terms of the AP: 54,51,48.... So that their
Sum is 513
...otodes of 8​

Answer 1

Answer:

Number of terms = 54,51,48,45,42,39,36,33,30,27,24,21,18,15,12,9,6,3, 0

Sum = 54+54+54+54+54+54+5+35

=413

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Answer 2

a=54

d=(-3)

S^n=513

now, using of S^n formula

S^n = n/2{2a+(n-1)d}

513=n/2{2*54+(n-1)-3}

513=n/2{108+(-3n+3)}

513=n/2{108-3n-3}

513*2=n(105-3n)

1026=105n-3n^2

3n^2-105n+1026=0

3(n^2-35n+342)=0

n^2-35n+342=0

n^2-19n-18n+342=0

n(n-19)-18(n-19)=0

(n-18)(n-19)=0

therefore no. of terms be 18 or 19