Advertisements
Advertisements
प्रश्न
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Advertisements
उत्तर
Given:
nth term of the A.P. 9, 7, 5... is the same as the nth term of the A.P. 15, 12, 9...
\[\text { Considering } 9, 7, 5...\]
\[a = 9, d = \left( 7 - 9 \right) = - 2\]
\[ n^{th} \text { term } = 9 + (n - 1)( - 2) \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ = 9 - 2n + 2\]
\[ = 11 - 2n . . . (i)\]
\[\text { Considering } 15, 12, 9, ...\]
\[a = 15, d = \left( 12 - 15 \right) = - 3\]
\[ n^{th} \text { term } = 15 + (n - 1)( - 3) \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ = 15 - 3n + 3\]
\[ = 18 - 3n . . . (ii)\]
Equating (i) and (ii), we get:
\[11 - 2n = 18 - 3n\]
\[ \Rightarrow n = 7\]
Thus, 7th terms of both the A.P.s are the same.
APPEARS IN
संबंधित प्रश्न
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 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
The Fibonacci sequence is defined by a1 = 1 = a2, an = an − 1 + an − 2 for n > 2
Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
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.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
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.
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of first n odd natural numbers.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of odd integers from 1 to 2001.
If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also 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.
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.
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 is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If m th term of an A.P. is n and nth term is m, then write its pth term.
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term 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:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
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
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
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)`
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
