Advertisements
Advertisements
प्रश्न
Is 68 a term of the A.P. 7, 10, 13, ...?
Advertisements
उत्तर
7, 10, 13...
Here, we have:
a = 7
\[d = \left( 10 - 7 \right) = 3\]
\[\text { Let } a_n = 68\]
\[ \Rightarrow a + (n - 1) d = 68\]
\[ \Rightarrow 7 + (n - 1)(3) = 68\]
\[ \Rightarrow (n - 1)(3) = 61\]
\[ \Rightarrow (n - 1) = \frac{61}{3}\]
\[ \Rightarrow n = \frac{61}{3} + 1 = \frac{64}{3}\]
Since n is not a natural number.So, 68 is not a term of the given A.P.
APPEARS IN
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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.
A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
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.
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.
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 sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of first n natural numbers.
Find the sum of all integers between 50 and 500 which are divisible by 7.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
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?
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are 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.
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 manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.
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.
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
Write the common difference of an A.P. the sum of whose first n terms is
If m th term of an A.P. is n and nth term is m, then write its pth term.
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 2 n2 + 5 n, then its nth term is
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 in an A.P., Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
The pth term of an A.P. is a and qth term is b. Prove that the sum of its (p + q) terms is `(p + q)/2[a + b + (a - b)/(p - q)]`.
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 ______.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
