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Suppose you are given the arithmetic sequence − 1 , 1 , 3 , 5 , ⋯ . How many consecutive terms of this sequence (starting from the first) must be added to obtain a sum of 80?

Sagot :

Answer: 10

Step-by-step explanation:

Use the formula for partial sum.

S

n

=

n

2

[

2

a

1

+

(

n

1

)

d

]

80

=

n

2

[

2

(

1

)

+

(

n

1

)

2

]

80

=

n

2

[

2

+

2

n

2

]

80

=

n

2

[

2

n

4

]

80

=

n

(

n

2

)

80

=

n

2

2

n

n

2

2

n

80

=

0

Solve this quadratic equation by factoring:

n

2

2

n

80

=

0

(

n

10

)

(

n

+

8

)

=

0

n

=

10

;

n

=

8

Since the number of terms in a sequence is always positive, we conclude that 10 terms of the sequence  

1

,

1

,

3

,

5

,

are added to obtain a sum of 80.