Advertisements
Advertisements
Question
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Advertisements
Solution
\[\text { Given }: \]
\[ a_k = 5k + 1\]
\[\text { For} k = 1, a_1 = 5 \times 1 + 1 = 6\]
\[\text { For }k = 2, a_2 = 5 \times 2 + 1 = 11\]
\[\text { For } k = n, a_n = 5n + 1\]
\[ \therefore S_n = \frac{n}{2}\left[ a + a_n \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 6 + 5n + 1 \right] = \frac{n}{2}\left( 5n + 7 \right)\]
APPEARS IN
RELATED QUESTIONS
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
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?
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
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?
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 manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
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, ...
Which term of the A.P. 4, 9, 14, ... is 254?
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.
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 second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of all even integers between 101 and 999.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
Insert five numbers between 8 and 26 such that the resulting sequence is an 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.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
The pth term of an A.P. is a and qth term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.
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
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
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)`
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
