Advertisements
Advertisements
Question
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
Advertisements
Solution
Given:
\[a_6 = 12\]
\[ \Rightarrow a + \left( 6 - 1 \right)d = 12\]
\[ \Rightarrow a + 5d = 12 . . . (i)\]
\[ a_8 = 22\]
\[ \Rightarrow a + \left( 8 - 1 \right)d = 22\]
\[ \Rightarrow a + 7d = 22 . . . (ii)\]
\[\text { Solving (i) and (ii), we get: } \]
\[2d = 10\]
\[ \Rightarrow d = 5\]
\[\text { Putting the value of d in (i), we get: } \]
\[ a + 5 \times 5 = 12\]
\[ \Rightarrow a = 12 - 25 = - 13\]
\[ \therefore a_2 = a + \left( 2 - 1 \right)d = a + d = - 13 + 5 = - 8\]
\[\text { Also,} a_n = a + (n - 1)d \]
\[ = - 13 + (n - 1)5\]
\[ = - 13 + 5 n - 5 \]
\[ = 5n - 18 \]
RELATED QUESTIONS
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)th numbers is 5:9. Find the value of m.
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
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?
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.
Is 302 a term of the A.P. 3, 8, 13, ...?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
How many numbers of two digit are divisible by 3?
The number of terms of an A.P. is even; the sum of odd terms is 24, of the even terms is 30, and the last term exceeds the first by \[10 \frac{1}{2}\] , find the number of terms and the series.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
Find the sum of odd integers from 1 to 2001.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
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.
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.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
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?
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?
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?
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 log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
Write the sum of first n odd natural numbers.
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
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
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:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
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 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
