Advertisements
Advertisements
Question
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Advertisements
Solution
Given:
\[a_6 = 19\]
\[ \Rightarrow a + \left( 6 - 1 \right)d = 19 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 5d = 19 . . \left( 1 \right)\]
\[\text { And,} a_{17} = 41\]
\[ \Rightarrow a + \left( 17 - 1 \right)d = 41 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 16d = 41 . . \left( 2 \right)\]
\[\text { Solving the two equations, we get, } \]
\[16d - 5d = 41 - 19\]
\[ \Rightarrow 11d = 22\]
\[ \Rightarrow d = 2 \]
\[\text { Putting d }= 2 \text { in the eqn } \left( 1 \right), \text { we get }: \]
\[a + 5 \times 2 = 19\]
\[ \Rightarrow a = 19 - 10\]
\[ \Rightarrow a = 9 \]
We know:
\[a_{40} = a + \left( 40 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ = a + 39d\]
\[ = 9 + 39 \times 2 \]
\[ = 9 + 78 = 87\]
APPEARS IN
RELATED QUESTIONS
Find the sum of odd integers from 1 to 2001.
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
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.
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?
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
−1, 1/4, 3/2, 11/4, ...
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the A.P. 4, 9, 14, ... is 254?
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.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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 \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] 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., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also 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.
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.
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 sum of n terms of an AP is 2n2 + 3n, then write its nth term.
Write the sum of first n even natural numbers.
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term 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
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that `(m + n) (1/m - 1/p) = (m + p) (1/m - 1/n)`
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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 ______.
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
