English

Find: 10th Term of the A.P. 1, 4, 7, 10, ... - Mathematics

Advertisements
Advertisements

Question

Find:

 10th term of the A.P. 1, 4, 7, 10, ...

Solution

1, 4, 7, 10...
We have:
a = 1
d =\[4 - 1 = 3\]

\[a_{10} = a + (10 - 1)d \left[ a_n = a + \left( n - 1 \right)d \right]\]

\[ = a + 9d \]

\[ = 1 + 9 \times 3 \]

\[ = 28\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 19: Arithmetic Progression - Exercise 19.2 [Page 11]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 1.1 | Page 11

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the sum of odd integers from 1 to 2001.


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.


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?


Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.


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.


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 = 1, an = an − 1 + 2, 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.

 


Find:

nth term of the A.P. 13, 8, 3, −2, ...


How many terms are there in the A.P. 7, 10, 13, ... 43 ?


The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.


\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]

\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]


Find the sum of the following arithmetic progression :

a + b, a − b, a − 3b, ... to 22 terms


Find the sum of the following arithmetic progression :

 (x − y)2, (x2 + y2), (x + y)2, ... to n terms


Find the sum of the following arithmetic progression :

\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.


Find the sum of the following serie:

101 + 99 + 97 + ... + 47


Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.


If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?


Find the sum of odd integers from 1 to 2001.


If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.


If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:

\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] 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 a, b, c is in A.P., prove that:

a2 + c2 + 4ac = 2 (ab + bc + ca)


If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that abc 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.


There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.


A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?


In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?


If m th term of an A.P. is n and nth term is m, then write its pth term.


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 sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =


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 \[\frac{S_1}{S_2}\] = 


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. 


If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad


In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term 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


If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.


The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×