Question

How many terms of the AP 45,39, 33, etc must be taken so that their sum is 180

Answer 1

Answer:

10 or 6

Step-by-step explanation:

Sum=n/2(2a+(n-1)d)

180=n/2(2*45+(n-1)-6)

180*2=n(90-6n+6)

360=n(96-6n)

360=96n-6n^2

Divide everything by 6

60=16n-n^2

Rearrange by taking everything to the left such that it finally equates to 0

n^2-16n+60=0

Factorise

Sum=-16,product=60

Factors=-10,-6

n^2-6n-10n+60=0

n(n-6)-10(n-6)=0

(n-10)(n-6)=0

n=10 or 6

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