7^(th) term of an A.P. is 40. Then, the ...

`7^(th)` term of an A.P. is 40. Then, the sum of first 13 terms is

A

520

B

53

C

2080

D

1040

Text Solution

Verified by Experts

The correct Answer is:

A

Let a be the first term and d be the common difference of the A.P. Then,
`a_(7)=40rArr a+6d=40`
Now,
`S_(13)=(13)/(2){2a+(13-1)=13(a+6d)=13xx40=520`

Topper's Solved these Questions

SEQUENCES AND SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|80 Videos
SEQUENCES AND SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos
QUADRATIC EXPRESSIONS AND EQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos
SETS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The sum of 3^(rd) and 11^(th) terms of an A.P. is 34. Find the sum of its 13 terms.

If 8^(th) of an A.P. is 15 , then the sum of first 15 terms is

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 ?

The sum of first p- terms terms of an A.P. is q and the sum of first q terms is p, find the sum of first (p + q)

If the first term of an A.P. is 2 and the sum of first five terms is equal to one-fourth of the sum of the next five terms, show that the 20th term is -112.

The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.

The sum of 5th and 9th term of an A.P. is 72 and the sum of 7th and 12th terms is 97 . Find that

The first term of an A.P. is 20 and the sum of its first seven terms is 2100, find the 31st term of this A.P.

The sum of first 7 terms of an A.P. is 49 and that of first 17 terms of it is 289. Find the sum of first n terms.

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test

7^(th) term of an A.P. is 40. Then, the sum of first 13 terms is
Text Solution
|
Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...
Text Solution
|
Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............
Text Solution
|
If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...
Text Solution
|
If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P....
Text Solution
|
Given that n arithmetic means are inserted between two sets of numbers...
Text Solution
|
If a,b, and c are in G.P then a+b,2b and b+ c are in
Text Solution
|
If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...
Text Solution
|
If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...
Text Solution
|
Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.
Text Solution
|
If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...
Text Solution
|
If Sn denotes the sum of n terms of an A.P. whose common difference is...
Text Solution
|
The sides of a right angled triangle are in A.P., then they are in the...
Text Solution
|
Find the sum of all the 11 terms of an AP whose middle most term is 30...
Text Solution
|
The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...
Text Solution
|
If three numbers are in G.P., then the numbers obtained by adding the ...
Text Solution
|
If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....
Text Solution
|
Let a,b,c be three positive prime number. The progrrssion in which sqr...
Text Solution
|
If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...
Text Solution
|
If three numbers are in H.P., then the numbers obtained by subtracting...
Text Solution
|
The first three of four given numbers are in G.P. and their last three...
Text Solution
|