Advertisements
Advertisements
प्रश्न
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
उत्तर
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,
\[\text { As, } a_2 - a_1 = 5520 - 5200 = 320 \text { and } a_3 - a_2 = 5840 - 5520 = 320\]
\[i . e . a_2 - a_1 = a_3 - a_2 \]
\[\text { So, } a_1 , a_2 , a_3 , . . . \text { are in A . P } . \]
\[\text { Also, } a = 5200, d = 320\]
\[\left( i \right) a_{10} = a + \left( 10 - 1 \right)d\]
\[ = 5200 + 9 \times 320\]
\[ = 5200 + 2880\]
\[ = 8080\]
\[\text { So, the salary of the man for the tenth month is } ₹ 8, 080 . \]
\[\left( ii \right) S_{12} = \frac{12}{2}\left[ 2a + \left( 12 - 1 \right)d \right]\]
\[ = 6\left( 2 \times 5200 + 11 \times 320 \right)\]
\[ = 6\left( 10400 + 3520 \right)\]
\[ = 6 \times 13920\]
\[ = 83520\]
\[\text { So, the total earnings of the man during the first year is } ₹ 83, 520 .\]
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Is 68 a term of the A.P. 7, 10, 13, ...?
Is 302 a term of the A.P. 3, 8, 13, ...?
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Find the sum of all odd numbers between 100 and 200.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
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 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 \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
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.
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.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?
Write the common difference of an A.P. whose nth term is xn + y.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
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.
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. Find his salary for the tenth month
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 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
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 ______.
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 ______.
