Advertisements
Advertisements
प्रश्न
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
विकल्प
3
2
6
4
Advertisements
उत्तर
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is 4.
Explanation:
Given that Sn = 3n + 2n2
S1 = 3(1) + 2(1)2 = 5
S2 = 3(2) + 2(4) = 14
S1 = a1 = 5
S2 – S1 = a2
= 14 – 5
= 9
∴ Common difference d = a2 – a1
= 9 – 5
= 4
APPEARS IN
संबंधित प्रश्न
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Let < an > be a sequence. Write the first five term in the following:
a1 = a2 = 2, an = an − 1 − 1, n > 2
Find:
10th term of the A.P. 1, 4, 7, 10, ...
Find:
18th term of the A.P.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]
Is 302 a term of the A.P. 3, 8, 13, ...?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
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.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
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.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
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.
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?
We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.
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?
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
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
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
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
