Advertisements
Advertisements
प्रश्न
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
Advertisements
उत्तर
Given:
\[a_6 = 19\]
\[ \Rightarrow a + \left( 6 - 1 \right)d = 19 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 5d = 19 . . \left( 1 \right)\]
\[\text { And,} a_{17} = 41\]
\[ \Rightarrow a + \left( 17 - 1 \right)d = 41 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow a + 16d = 41 . . \left( 2 \right)\]
\[\text { Solving the two equations, we get, } \]
\[16d - 5d = 41 - 19\]
\[ \Rightarrow 11d = 22\]
\[ \Rightarrow d = 2 \]
\[\text { Putting d }= 2 \text { in the eqn } \left( 1 \right), \text { we get }: \]
\[a + 5 \times 2 = 19\]
\[ \Rightarrow a = 19 - 10\]
\[ \Rightarrow a = 9 \]
We know:
\[a_{40} = a + \left( 40 - 1 \right)d \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ = a + 39d\]
\[ = 9 + 39 \times 2 \]
\[ = 9 + 78 = 87\]
APPEARS IN
संबंधित प्रश्न
if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.
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 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.
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the A.P. 84, 80, 76, ... is 0?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
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 odd numbers between 100 and 200.
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all integers between 50 and 500 which are divisible by 7.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
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.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
a (b +c), b (c + a), c (a +b) are in A.P.
If x, y, z are in A.P. and A1 is the A.M. of x and y and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
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.
Write the common difference of an A.P. whose nth term is xn + y.
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
If m th term of an A.P. is n and nth term is m, then write its pth term.
In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
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.
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
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
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
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
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 ______.
