Advertisements
Advertisements
प्रश्न
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Advertisements
उत्तर
Given:
\[a_{10 =} 41\]
\[ \Rightarrow a + \left( 10 - 1 \right)d = 41 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 9d = 41 \]
\[\text { And }, a_{18} = 73\]
\[ \Rightarrow a + \left( 18 - 1 \right)d = 73 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 17d = 73 \]
\[\text { Solving the two equations, we get }: \]
\[ \Rightarrow 17d - 9d = 73 - 41\]
\[ \Rightarrow 8d = 32\]
\[ \Rightarrow d = 4 . . . (i)\]
\[\text { Putting the value in first equation, we get }: \]
\[a + 9 \times 4 = 41\]
\[ \Rightarrow a + 36 = 41\]
\[ \Rightarrow a = 5 . . . (ii)\]
\[a_{26} = a + \left( 26 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a_{26} = a + 25d \]
\[ \Rightarrow a_{26} = 5 + 25 \times 4 \left( \text { From } (i) \text { and } (ii) \right)\]
\[ \Rightarrow a_{26} = 5 + 100 = 105\]
संबंधित प्रश्न
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.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 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.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the A.P. 4, 9, 14, ... is 254?
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
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.
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
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 :
41, 36, 31, ... 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 all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all integers between 84 and 719, which are multiples of 5.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th 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.
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?
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term 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
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
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
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 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 ______.
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 ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
