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
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?
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
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 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.
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 = a2 = 2, an = an − 1 − 1, n > 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
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.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
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.
Find the sum of all integers between 50 and 500 which are divisible by 7.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
If a, b, c is in A.P., then show that:
bc − a2, ca − b2, ab − c2 are in A.P.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
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.
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 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 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.
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
If m th term of an A.P. is n and nth term is m, then write its pth term.
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If Sn denotes the sum of first n terms of an A.P. < an > such that
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
