Question

How many terms of an AP 6,-11/2,5are need to give their sum - 25

Answer 1

Answer:

It is known that, S

n

=

20

n

[2a+(n−1)d],

where n= number of terms , a= first term, and d= common difference

Here, a=−6,d=

2

1

⇒−25=

2

n

[2×(−6)+(n−1)(

2

1

)]

⇒−50=n[−12+

2

n

−

2

1

]

⇒−50=n[−

2

25

+

2

n

]

⇒−100=n(−25+n)

⇒n

2

−25n+100=0

⇒n

2

−5n−20n+100=0

⇒n(n−5)−20(n−5)=0

⇒n=20

⇒n=5

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