Advertisements
Advertisements
प्रश्न
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Advertisements
उत्तर
\[a_n = 2n + 7\]
\[ \therefore a_1 = 2 \times 1 + 7 = 9\]
\[ a_2 = 2 \times 2 + 7 = 11\]
\[ a_3 = 2 \times 3 + 7 = 13\]
\[ a_4 = 2 \times 4 + 7 = 15\]
\[\text { and so on }\]
\[\text { So, common difference }\left( d \right) = 11 - 9 = 2\]
\[\text { Thus, the above sequence is an A . P . with the common difference as} 2\]
\[ a_7 = 2 \times 7 + 7 = 21\]
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
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, ...
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, ...
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
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 three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
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.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
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 x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
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.
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?
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
Write the sum of first n odd natural numbers.
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
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
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
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.
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
Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
Which of the following is an example of a Constant A.P.?
If you save ₹500 in the first month, ₹700 in the second month, ₹900 in the third month, and so on, what is the common difference of the A.P. \(500, 700, 900, 1100, \ldots\)?
