Advertisements
Advertisements
Question
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, ...
Advertisements
Solution
\[\text { We have: } \]
\[1/4 - ( - 1) = 5/4\]
\[3/2 - 1/4 = 5/4\]
\[11/4 - 3/2 = 5/4\]
\[\text { Thus, the sequence is an A . P . with the common difference being } (5/4) . \]
\[\text { The next three terms are as follows }: \]
\[11/4 + 5/4 = 16/4 = 4\]
\[16/4 + 5/4 = 21/4\]
\[21/4 + 5/4 = 26/4\]
APPEARS IN
RELATED QUESTIONS
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`
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
3, −1, −5, −9 ...
Which term of the A.P. 4, 9, 14, ... is 254?
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
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 sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of all even integers between 101 and 999.
Find the sum of the series:
3 + 5 + 7 + 6 + 9 + 12 + 9 + 13 + 17 + ... to 3n terms.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
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.
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
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.
Write the common difference of an A.P. the sum of whose first n terms is
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 m th term of an A.P. is n and nth term is m, then write its pth term.
In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n 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
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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?
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 ______.
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 ______.
