Advertisements
Advertisements
Question
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Advertisements
Solution
1, 4, 7, 10...
We have:
a = 1
d =\[4 - 1 = 3\]
\[a_{10} = a + (10 - 1)d \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ = a + 9d \]
\[ = 1 + 9 \times 3 \]
\[ = 28\]
RELATED QUESTIONS
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
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.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
Is 302 a term of the A.P. 3, 8, 13, ...?
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
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 the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all even integers between 101 and 999.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
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?
A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
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?
Write the common difference of an A.P. whose nth term is xn + y.
Write the sum of first n odd natural numbers.
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
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 a1, a2, a3, .... an are in A.P. with common difference d, then the sum of the series sin d [sec a1 sec a2 + sec a2 sec a3 + .... + sec an − 1 sec an], is
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , 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 =
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
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. What is his total earnings during the first year?
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 ______.
