The `1^(st)` , `2^(nd)` and `3^(rd)` terms of an arithmetic series are `a`, `b` and `a^(2)` where `'a'` is negative. The `1^(st)`, `2^(nd)` and `3^(rd)` terms of a geometric series are `a`, `a^(2)` and `b` respectively. The sum of infinite geometric series is
A
`(-1)/(2)`
B
`(-3)/(2)`
C
`(-1)/(3)`
D
None of these
Text Solution
Verified by Experts
The correct Answer is:
C
`(c )` `a,b,a^(2)`,……is an `A.P.` `:. 2b=a^(2)+a`…..`(i)` `a,a^(2),b`,………is a `G.P.` `:.a^(3)=b`…….`(ii)` `:.a^(2)+a=2a^(3)` `:.a=0`, `a=1` or `a=-1//2` `:.a=-1//2` (as `a lt 0`) `:.b=-(1)/(8)` In `G.P.` putting `a=-(1)/(2)` and `b=-(1)/(8)` `:. G.P.` is `-(1)/(2),(1)/(4),-(1)/(8)`... Sum of infinite `G.P.=(a)/(1-r)=(-(1)/(2))/(1-(((1)/(4))/((-1)/(2))))=(-1)/(3)` Sum of `40` terms of `A.P.=(n)/(2)[2a+(n-1)d]` `=(40)/(2)[2((-1)/(2))+(40-1)xx(-(1)/(8)+(1)/(2))]` `=20[-1+39xx(3)/(8)]` `=(545)/(2)`
The 1^(st) , 2^(nd) and 3^(rd) terms of an arithmetic series are a , b and a^(2) where 'a' is negative. The 1^(st) , 2^(nd) and 3^(rd) terms of a geometric series are a , a^(2) and b respectively. The sum of the 40 terms of the arithmetic series is
The 1^(st),2^(nd) and 3^(rd) terms of an arithme tic series are a a and a^(2) where 'a' is negative.The 1^(st),2^(nd),3^(rd) terms of a geometric series are a,a^(2) and b find the value of a and b
The 1^st, 2^nd and 3^rd terms of an arithmetic series are a, b and a^2 where 'a' is negative. The 1^st, 2^nd and 3^rd terms of a geometric series are a, a^2 and b find the (a) value of a and b (b) sum of infinite geometric series if it exists. If no then find the sum to n terms of the G.P. (c) sum of the 40 term of the arithmetic series.
Find the sum of the infinite geometric series 1+3x+9x^2+27x^3+…..
The 1st, 2nd and 4th terms of a proportion are 12, 21 and 14 respectively. Its third term is
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CENGAGE-PROGRESSION AND SERIES-ARCHIVES (MATRIX MATCH TYPE )
