Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
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?
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?
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.
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
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.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
Find the sum of all even integers between 101 and 999.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
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.
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
Write the sum of first n odd natural numbers.
If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
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 Sn denotes the sum of first n terms of an A.P. < an > such that
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
If a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [cosec a1cosec a2 + cosec a1 cosec a3 + .... + cosec an − 1 cosec an] 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
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 sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
Mark the correct alternative in the following question:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
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 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 ____________.
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
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?
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
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 ______.
