Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic progression :
1, 3, 5, 7, ... to 12 terms
Advertisements
उत्तर
1, 3, 5, 7 ... to 12 terms
\[\text { We have }: \]
\[ a = 1, d = \left( 3 - 1 \right) = 2\]
\[n = 12\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ = \frac{12}{2}\left[ 2 \times 1 + (12 - 1)(2) \right]\]
\[ = 6\left[ 24 \right] = 144\]
APPEARS IN
संबंधित प्रश्न
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
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 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 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.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
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.
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Find:
nth term of the A.P. 13, 8, 3, −2, ...
Is 302 a term of the A.P. 3, 8, 13, ...?
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.
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.
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
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.
\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]
\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
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 n terms of the A.P. whose kth terms is 5k + 1.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
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.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
Write the sum of first n even natural numbers.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If m th term of an A.P. is n and nth term is m, then write its pth term.
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
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?
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
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 ______.
