Advertisements
Advertisements
Question
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
Advertisements
Solution
The first installment of the loan is Rs 100.
The second installment of the loan is Rs 105 and so on.
The amount that the man repays every month forms an A.P.
The A.P. is 100, 105, 110, …
First term, a = 100
Common difference, d = 5
A30 = a + (30 – 1)d
= 100 + (29) (5)
= 100 + 145
= 245
Thus, the amount to be paid in the 30th installment is Rs 245.
RELATED QUESTIONS
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
−1, 1/4, 3/2, 11/4, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Is 68 a term of the A.P. 7, 10, 13, ...?
Is 302 a term of the A.P. 3, 8, 13, ...?
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
a (b +c), b (c + a), c (a +b) are in A.P.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If m th term of an A.P. is n and nth term is m, then write its pth term.
If Sn denotes the sum of first n terms of an A.P. < an > such that
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
