Question

How many terms of the AP 16, 14.12... are needed to give the sum 60?
Explain why do we get two answers ​

Answer 1

Answer:

Step-by-step explanation:

16,14,12

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

60=n/2{2*16+(n-1)(-2)}

120=n{34-2n}

120=34n-2n2

n2 -17n+60=0

n2 -12n-5n+60=0

n(n-12)-5(n-12)=0

n=5,12

here,the common difference is negative therefore terms go on diminishing and 9th term becomes zero.

All terms after 9th term are negative.These negative terms when added to positive terms from 6th to 8th term,they cancel out each other and the sum remains same.

Answer 2

Answer:

You get n as 12 and 5

Both are correct because the series is in decreasing order and so some terms goes to negative and that's going to cancel out giving you same sum as 60.

To understand once write the 12 terms and check the count along with 5 terms.

Hope it helps.

Mark Brainer.

Thanks.

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Teacher.