Math, asked by kimkim23, 9 months ago

A man repays a debt of Rs 4860 by paying Rs 30 in the first month and then increases the amount by Rs 15 every month.How long will it take time to clear the debt(Assume that no interest is charged)?​

Answers

Answered by raj2652004
3

Answer:

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Step-by-step explanation:

Arithmetic sequences are the sequences which have a constant difference between the numbers. In other words, it is the sequence of numbers in which we obtain the next term by adding a constant number.So, it is in the form of

(

a

,

a

+

d

,

a

+

2

d

,

a

+

3

d

...

.

For example,

3

,

5

,

7

,

9

,

11

,

13

...

Is an arithmetic sequence. In this the common difference is

2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, let's understand this question. In this, he pays

3250

by giving

20

in the first month. And then, increases it by

15

every month thereafter.

20

,

35

,

50

,

65

...

.

In this manner he clears the loan in

n

months

To solve this, we need to know the formula

S

n

=

n

2

(

2

a

+

(

n

1

)

d

)

Where,

S

n

is the sum of

n

number of terms.

a

is the first term(

20

). And,

d

is the common difference (In this case, it is

15

). Finally,

n

is the number of terms

According to the question, We need to find

n

. And also, they have given

S

n

=

3250

So,

S

n

=

n

2

(

2

a

+

(

n

1

)

d

)

3250

=

n

2

(

2

(

20

)

+

(

n

1

)

(

15

)

)

n

(

40

+

15

n

15

)

=

2

×

3250

n

(

25

+

15

n

)

=

6500

15

n

2

+

25

n

6500

=

0

3

n

2

+

5

n

1300

=

0

(

n

20

)

(

3

n

+

65

)

=

0

n

20

=

0

n

=

20

months

Answered by ashutoshdash001
0

Answer:

Suppose the loan is cleared in n months. Clearly, the amounts form an A.P. with first term 20 and the common difference 15.

∴ Sum of the amounts =3250

2

n

{2×20+(n−1)×15}=3250

2

n

(40+15n−15)=3250

⟹n(15n+25)=6500

⟹15

2

+25n−6500=0

⟹3n

2

+5n−1300=0

⟹(n−20)(3n+65)=0

⟹n=20 or, n=−

3

65

⟹n=20 [∵n

=

3

65

]

Thus, the loan is cleared in 20 months

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