Advertisements
Advertisements
प्रश्न
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
Advertisements
उत्तर
a1 = 1, an = an − 1 + 2, n ≥ 2
\[a_2 = a_1 + 2 = 1 + 2 = 3\]
\[ a_3 = a_2 + 2 = 5\]
\[ a_4 = a_3 + 2 = 7\]
\[ a_5 = a_4 + 2 = 9\]
Hence, the five terms are 1, 3, 5, 7 and 9.
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
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`
if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
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.
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?
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.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Which term of the A.P. 84, 80, 76, ... is 0?
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:
1, 4, 7, 10, ..., 88
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
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.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following arithmetic progression :
41, 36, 31, ... to 12 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of all odd numbers between 100 and 200.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
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 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.
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.
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
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 the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], is
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
