Advertisements
Advertisements
Question
Is 302 a term of the A.P. 3, 8, 13, ...?
Advertisements
Solution
3, 8, 13...
Here, we have:
a = 3
\[d = \left( 8 - 3 \right) = 5\]
\[\text { Let }a_n = 302\]
\[ \Rightarrow a + \left( n - 1 \right)d = 302\]
\[ \Rightarrow 3 + \left( n - 1 \right)5 = 302\]
\[ \Rightarrow \left( n - 1 \right)5 = 299\]
\[ \Rightarrow \left( n - 1 \right) = \frac{299}{5}\]
\[ \Rightarrow n = \frac{299}{5} + 1 = \frac{304}{5}\]
Since n is not a natural number.So, 302 is not a term of the given A.P.
RELATED QUESTIONS
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
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 person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
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.
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Which term of the A.P. 4, 9, 14, ... is 254?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
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.
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.
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 :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of all odd numbers between 100 and 200.
Find the sum of n terms of the A.P. whose kth terms is 5k + 1.
In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.
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 \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
bc, ca, ab are in A.P.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
Write the common difference of an A.P. the sum of whose first n terms is
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 \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 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 the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is
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
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
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 ______.
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
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 ______.
Which of the following is an example of a Constant A.P.?
