Home
Class 11
MATHS
The sum of first three terms of a G.P is...

The sum of first three terms of a G.P is `(39)/(10)` and their product is 1. Find the common ratio and the terms.

Text Solution

Verified by Experts

Let terms be `(a)/(r)` a,ar
Given `(a)/(r)."a.ar"=1rArra^(3)=1rArra=1`
Also `(a)/(r)+a+"ar"=(39)/(10)rArr(1)/(r)+1+r=(39)/(10)`
`rArr10+10r+10r^(2)=39r`
`rArr10r^(2)-29r+10=0`
`rArr(2r-5)(5r-2)=0rArrr=(5)/(2)or(2)/(5)`
When `a=1,r=(2)/(5),(a)/(r)a,"ar"=(5)/(2),1,(2)/(5)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    SUBHASH PUBLICATION|Exercise solved example (FIVE MARKS QUESTIONS WITH ANSWERS)|9 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise FIVE MARKS QUESTIONS WITH ANSWERS|8 Videos

  • SETS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESETION WITH ANSWERERS|15 Videos

Similar Questions

Explore conceptually related problems

The sum of first three terms of a G.P. is ( 13)/(12) and their product is -1 Find the common ratio and the terms

The sum of first three terms of a G.P. is 13/12 and their product is – 1. Find the common ratio and the terms.

The sum of first three of a G.P is (13)/(12) and their product is -1 . Find the common ratio and the terms.

The sum of the third and seventh terms of an A.P is 6 and their product is 8 find the sum of first sixteen terms of the A.P.

If the sum of first term of an A.P is 49 and that of 17 terms is 289. Find the sum of first "n" terms. OR The sum of the third and seyenth terms of an AP is 6 and their product is 8. find the sum of first sixteen terms of the A.P.

The sum of the third and seventh terms of an AP is 6 and their product is 8 find the sum of first sixteen terms of the A.P.

The sum of first 14 terms of an AP is 1505 and its first term is 10. Find its tenth term.

The sum of the third and the seventh terms of an A.P. is 6 and the product is 8. Find the sum of first sixteen terms of the A.P.

The sum of first three terms of a G.P is 16 and the sum of the next three terms is 128 Determine the first term, the common ratio and the sum to n terms of the G.P.

The sum of the first three terms of an A.P is 33 . If the product of the first terms and third term exceeds the 2nd term by 29 then find the A.P . The pth qth and rth term of an A.P . Are a b and c respectively . Prove that a (q-r)+ b(r-P)+c(p-q)=0