Advertisements
Advertisements
Question
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.
Advertisements
Solution
\[\text { Let the three terms of the A . P . be }a - d, a, a + d . \]
\[\text { Then, we have }: \]
\[a - d + a + a + d = 21\]
\[ \Rightarrow 3a = 21\]
\[ \Rightarrow a = 7 . . . . (i)\]
\[\text { Also }, (a - d)(a + d) - a = 6\]
\[ \Rightarrow a^2 - d^2 - a = 6\]
\[ \Rightarrow 49 - d^2 - 7 = 6\]
\[ \Rightarrow 36 = d^2 \]
\[ \Rightarrow \pm 6 = d\]
\[\text { When } d = 6, a = 7, \text { we get} : \]
\[1, 7, 13\]
\[\text { When } d = - 6, a = 7, \text{we get }: \]
\[13, 7, 1\]
APPEARS IN
RELATED QUESTIONS
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
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 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.
If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
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.
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of the following arithmetic progression :
(x − y)2, (x2 + y2), (x + y)2, ... to n terms
Find the sum of all even integers between 101 and 999.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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 saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?
Write the common difference of an A.P. the sum of whose first n terms is
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
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 n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3 : 29, then the value of n is
If in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
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
Mark the correct alternative in the following question:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
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 A.P. and x, y, z are in G.P., then the value of xb − c yc − a za − b is
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)]`.
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`
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. Find his salary for the tenth month
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 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.
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 ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
