Advertisements
Advertisements
Question
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
Advertisements
Solution
Let the number of terms of the given A.P. be n, first term be a and the common difference be d.
First term a = 2
Last term l = 50
Sum of all the terms Sn = 442
We know that,
Sum of the n terms Sn = `n/2(a + l)`
`=> 442 = n/2 (2 + 50)`
`=> 442 = n(26)`
`=> n = 442/26`
⇒ n = 17
Also,
l = a + (n - 1)d
Therefore,
On substituting the values of a, l and n, we get,
50 = 2 + (17 - 1)d
⇒ 50 = 2 + 16d
⇒ 50 - 2 = 16d
⇒ 48 = 16d
⇒ `48/16` = d
⇒ d = 3
Hence, the common difference of the given A.P. is 3.
APPEARS IN
RELATED QUESTIONS
Find the sum of odd integers from 1 to 2001.
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.
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 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 man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
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, ...
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
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.
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the sum of odd integers from 1 to 2001.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?
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?
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 sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
Write the sum of first n odd natural numbers.
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 four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
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 a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
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
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 a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an
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 ______.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.
