Advertisements
Advertisements
प्रश्न
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Advertisements
उत्तर
Given:
\[a_{10 =} 41\]
\[ \Rightarrow a + \left( 10 - 1 \right)d = 41 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 9d = 41 \]
\[\text { And }, a_{18} = 73\]
\[ \Rightarrow a + \left( 18 - 1 \right)d = 73 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 17d = 73 \]
\[\text { Solving the two equations, we get }: \]
\[ \Rightarrow 17d - 9d = 73 - 41\]
\[ \Rightarrow 8d = 32\]
\[ \Rightarrow d = 4 . . . (i)\]
\[\text { Putting the value in first equation, we get }: \]
\[a + 9 \times 4 = 41\]
\[ \Rightarrow a + 36 = 41\]
\[ \Rightarrow a = 5 . . . (ii)\]
\[a_{26} = a + \left( 26 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a_{26} = a + 25d \]
\[ \Rightarrow a_{26} = 5 + 25 \times 4 \left( \text { From } (i) \text { and } (ii) \right)\]
\[ \Rightarrow a_{26} = 5 + 100 = 105\]
APPEARS IN
संबंधित प्रश्न
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?
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, ...
Find:
nth term of the A.P. 13, 8, 3, −2, ...
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the sum of all integers between 84 and 719, which are multiples of 5.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
Insert five numbers between 8 and 26 such that the resulting sequence is an 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 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 carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
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?
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?
Write the common difference of an A.P. the sum of whose first n terms is
Write the sum of first n even natural numbers.
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
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
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?
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
The sum of terms equidistant from the beginning and end in an A.P. 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 ______.
