###### Advertisements

###### Advertisements

A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?

###### Advertisements

#### Solution

As each installment being less that the preceding installment by Rs. 10 the

installments are in A.P.

S_{12} = 1000 + 140 = 1140

n = 12, d = -10

`s_n=n/2[2a+(n-1)d]`

`s_12=12/2[2a+(11)(-10)]`

`1140=6[2a-110]`

`1140/6=[2a-110]`

190=[2a-110]

2a=190+110

2a=300

a=300/2

a=150

The first installment = Rs. 150.

#### APPEARS IN

#### RELATED QUESTIONS

Write the first three terms of the A.P. whose common difference is ‒3 and first term is 4.

There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the twenty-fifth row.

If m times m^{th} term of an A.P. is equal to n times its n^{th} term, then show that (m + n)^{th} term of the A.P. is zero.

An arithmetic progression 5, 12, 19, …. has 50 terms. Find its last term. Hence find the sum of its last 15 terms.

The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms:

0, - 4, - 8, - 12 …

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms:

1, 3, 9, 27 …

State whether the following sequence is an Arithmetic Progression or not:

3, 6, 12, 24,......

Find next two terms of an A.P.

4, 9, 14, ......

If `S_5 = 15` and `S_6 = 21`, Find `t_6`.

The general term of a sequence is given by a_{n} = −4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference.

Write the sequence with *n*th term: a_{n} = 9 − 5n

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

12, 2, −8, −18, ...

Find the n^{th} term of the A.P. 13, 8, 3, −2, ...

Find the arithmetic progression whose third term is 16 and the seventh term exceeds its fifth term by 12.

The first term and the common difference of an A. P. is 10,000 and

2000 resectively. Find the sum of first 12 terms of the A.P.

Check whether the following sequence is in A.P.

a – 3, a – 5, a – 7, …

Check whether the following sequence is in A.P.

1, –1, 1, –1, 1, –1, …

First term a and common difference d are given below. Find the corresponding A.P.

a = 7, d = – 5

Find the first term and common difference of the Arithmetic Progressions whose n^{th} term is given below

t_{n} = 4 – 7n

Find the 19^{th} term of an A.P. – 11, – 15, – 19, ...

Which term of an A.P. 16, 11, 6, 1, ... is – 54?

If 3 + k, 18 – k, 5k + 1 are in A.P. then find k

Priya earned ₹ 15,000 in the first month. Thereafter her salary increased by ₹ 1500 per year. Her expenses are ₹ 13,000 during the first year and the expenses increase by ₹ 900 per year. How long will it take for her to save ₹ 20,000 per month

Find the 12^{th} term from the last term of the A.P – 2, – 4, – 6, … – 100

Two A.P.’s have the same common difference. The first term of one A.P. is 2 and that of the other is 7. Show that the difference between their 10^{th} terms is the same as the difference between their 21^{st} terms, which is the same as the difference between any two corresponding terms.

One person borrows ₹ 4,000 and agrees to repay with a total interest of ₹ 500 in 10 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the first and the last instalments?

**Choose the correct alternative answer for the following sub question**

Find d of an A.P. whose first two terms are – 3 and 4

Find common difference of an A.P., 0.9, 0.6, 0.3 ......

Find d if t_{9} = 23 व a = 7

Which term of following A.P. is −940.

50, 40, 30, 20 ........

Activity :- Here a = `square`, d = `square`, t_{n} = −940

According to formula, t_{n} = a + (n − 1)d

−940 = `square`

n = `square`

t_{19} = ? for the given A.P., 9, 4, −1, −6 ........

Activity :- Here a = 9, d = `square`

t_{n} = a + (n − 1)d

t_{19} = 9 + (19 − 1) `square`

= 9 + `square`

= `square`

1, 6, 11, 16 ...... Find the 18^{th} term of this A.P.

For an A.P., t_{4 }= 12 and its common difference d = – 10, then find t_{n }

Find 27^{th} and n^{th} term of given A.P. 5, 2, – 1, – 4, ......

Find the first terms and common difference of an A.P. whose t_{8} = 3 and t_{12} = 52.

Which of the following form an AP? Justify your answer.

11, 22, 33,...

If six times of the 3^{rd} term is equal to the eight times of 7^{th} term in an A.P., then what will be the 19^{th} term?