Advertisements
Advertisements
प्रश्न
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
Advertisements
उत्तर
Let
\[S_{40}\] denote the total loan amount to be paid in 40 annual instalments.
∴ \[S_{40}\] = 3600
Let Rs a be the value of the first instalment and Rs d be the common difference.
We know:
\[S_n = \frac{n}{2}\left\{ 2a + \left( n - 1 \right)d \right\}\]
\[\Rightarrow \frac{40}{2}\left\{ 2a + \left( 40 - 1 \right)d \right\} = 3600\]
\[ \Rightarrow 20\left\{ 2a + 39d \right\} = 3600\]
\[ \Rightarrow 2a + 39d = 180 . . . . . . \left( 1 \right)\]
\[\text { Also, } S_{40} - S_{30} = \frac{1}{3} \times 3600\]
\[ \Rightarrow 3600 - S_{30} = 1200\]
\[ \Rightarrow S_{30} = 2400\]
\[ \Rightarrow \frac{30}{2}\left\{ 2a + \left( 30 - 1 \right)d \right\} = 2400\]
\[ \Rightarrow 15\left\{ 2a + 29d \right\} = 2400\]
\[ \Rightarrow 2a + 29d = 160 . . . . . \left( 2 \right)\]
On solving equations \[\left( 1 \right) \text { and } \left( 2 \right)\]
we get:
d = 2 and a =51
Hence, the value of the first instalment is Rs 51
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, 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.
9, 7, 5, 3, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Which term of the A.P. 4, 9, 14, ... is 254?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
How many numbers of two digit are divisible by 3?
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by \[10 \frac{1}{2}\] , find the number of terms and the series.
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.
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
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 accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
If a, b, c are in A.P. and x, y, z are in G.P., then the value of xb − c yc − a za − b is
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n
If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.
