Home
Class 12
MATHS
Two arithmetic progressions have the sam...

Two arithmetic progressions have the same numbers. The reatio of the last term of the first progression to the first term of the second progression is equal to the ratio of the last term of the second progression to the first term of first progression is equal to 4. The ratio of the sum of the n terms of the first progression to the sum of the n terms of teh first progression to the sum of the n terms of the second progerssion is equal to 2.
The ratio of their first term is

A

last term = 210

B

first term = 191

C

sum = 4010

D

sum =4200

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Last term in the nth row is
`1+2+3+…+n=1/2n(n+1)(1)`
As terms in the nth row forms an A.P. with common differences 1,so
First term = Last term -(n-1) (1)
`=1/2n(n+1)-n+1`
`=1/2(n^(2)-n+2)` (2)
Sum of terms`=1/2n[1/2(n^(2)-n+2)+1/2(n^(2)+n)]`
`=1/2n(n^(2)+1)`
Now, put n=20 in (1),(2),(3) to get required answers.
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Numerical)|27 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

Find the sum of first 20 terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77.

Find the sum of the first 20 terms of the arithmetic progression having the sum of first ten terms as 52 and the sum of the first 15 terms as 77.

In an arithmetic progression, the 24^(th) term is 100. Then the sum of the first 47 terms of the arithmetic progression is

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.

The third term of a geometric progression is 4. Then find the product of the first five terms.

In a GP , the ratio of the sum of the first eleven terms of the sum of the last even terms is 1//8 and the ratio of the sum of all the terms without the first nine to the sum of all terms without the last nine is 2 . Then the number of terms in the GP is

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.

the sum of the first n terms of a sequence is an^(2) + bn . Then the sum of the next n terms is