Advertisements
Advertisements
Question
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?
Advertisements
Solution
We have,
the initial salary, a1 = ₹5200,
the salary of the second month, a2 = ₹5200 + ₹320 = ₹5520,
the salary of the third month, a3 = ₹5520 + ₹320 = ₹5840,
\[\text { As, } a_2 - a_1 = 5520 - 5200 = 320 \text { and } a_3 - a_2 = 5840 - 5520 = 320\]
\[i . e . a_2 - a_1 = a_3 - a_2 \]
\[\text { So, } a_1 , a_2 , a_3 , . . . \text { are in A . P } . \]
\[\text { Also, } a = 5200, d = 320\]
\[\left( i \right) a_{10} = a + \left( 10 - 1 \right)d\]
\[ = 5200 + 9 \times 320\]
\[ = 5200 + 2880\]
\[ = 8080\]
\[\text { So, the salary of the man for the tenth month is } ₹ 8, 080 . \]
\[\left( ii \right) S_{12} = \frac{12}{2}\left[ 2a + \left( 12 - 1 \right)d \right]\]
\[ = 6\left( 2 \times 5200 + 11 \times 320 \right)\]
\[ = 6\left( 10400 + 3520 \right)\]
\[ = 6 \times 13920\]
\[ = 83520\]
\[\text { So, the total earnings of the man during the first year is } ₹ 83, 520 .\]
APPEARS IN
RELATED QUESTIONS
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.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
Which term of the A.P. 3, 8, 13, ... is 248?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
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 :
3, 9/2, 6, 15/2, ... to 25 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 serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
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 a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
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 manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
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.
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is
If Sn denotes the sum of first n terms of an A.P. < an > such that
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] is
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
Mark the correct alternative in the following question:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
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 ______.
