# The sum of father's and mother's ages is 84. if the age of father 5 years ago is the same as the age of mother 3 years later, how old is father now?

Answers: 3

## Answers

The sum of father's and mother's ages is 84. if the age of father 5 years ago is the same as the age...

answer:

step-by-step explanation: step 1: find the number of terms

the nth term of an arithmetic sequence is given by

t

n

=

a

+

(

n

−

1

)

d

. we know

t

n

(-57), r (-5) and a (8), however we don't know n. we will therefore solve for

n

.

−

57

=

8

+

(

n

−

1

)

−

5

−

57

=

8

−

5

n

+

5

−

57

−

13

=

−

5

n

−

70

=

−

5

n

n

=

14

∴

the sequence has

14

terms.

step 2: apply the formula for sum:

when dealing with arithmetic series, we will frequently use two formulas to help us find the sum. they are:

•

s

n

=

n

2

(

2

a

+

(

n

−

1

)

d

)

•

s

n

=

n

2

(

a

+

t

n

)

since we know the first term, the last term and the number of terms, we have enough information to use the latter; this one is more efficient and easy to use than the first.

s

n

=

n

2

(

a

+

t

n

)

s

14

=

14

2

(

8

+

(

−

57

)

)

s

14

=

7

(

8

−

57

)

s

14

=

−

343

hence, the sum of this arithmetic sequence is

−

343

.

practice exercises:

determine the sum of the following sequence:

3

,

14

,

25

,

,

179

hopefully this helps, and good luck!

dikit dikit mo nalang bawal kasi naka higa eh

2. f*g

3. fog

4. f+g

5. f/g

6. f-g

=11,200

time = i/(pr)

= 11,200/(40,000)(0.12)

= 11,200 / 4,800

= 2.33 or 2 years and 4 months