Advertisements
Advertisements
प्रश्न
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
Advertisements
उत्तर
7, 10, 13...43 Here, we have:
a = 7
\[d = (10 - 7) = 3\]
\[ a_n = 43\]
Let there be n terms in the given A.P.
\[\text { Also }, a_n = a + \left( n - 1 \right)d\]
\[ \Rightarrow 43 = 7 + \left( n - 1 \right)3\]
\[ \Rightarrow 36 = \left( n - 1 \right)3\]
\[ \Rightarrow 12 = \left( n - 1 \right)\]
\[ \Rightarrow 13 = n\]
Thus, there are 13 terms in the given A.P.
संबंधित प्रश्न
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
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.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
−1, 1/4, 3/2, 11/4, ...
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
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.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
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.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
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 :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
41, 36, 31, ... to 12 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of first n natural numbers.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab 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 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?
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
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 Sn denotes the sum of first n terms of an A.P. < an > such that
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
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
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 ______.
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
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 ______.
Which of the following best defines an Arithmetic Progression (A.P.)?
Which of the following is an example of a Constant A.P.?
If you save ₹500 in the first month, ₹700 in the second month, ₹900 in the third month, and so on, what is the common difference of the A.P. \(500, 700, 900, 1100, \ldots\)?
