Excercise 12C
A GP consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places, find the common ratio of the GP
The 4th and 7th terms of a GP are ????/ ???????? and ???? /???????????? respectively. Find the sum of n terms of the GP.
The 2nd and 5th terms of a GP are −1/2 and 1/16 respectively. Find the sum of n terms
How many terms of the series 2 + 6 + 18 + …. + must be taken to make the sum equal to 728?
Sum of a G.P. series is represented by the formula, when r>1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’...
Find the sum of the geometric series 3 + 6 + 12 + … + 1536.
Answer : Tn represents the nth term of a G.P. series. r = 6 ÷ 3 = 2 Tn = arn-1 ⇒1536 = 3 × 2n-1 ⇒1536 ÷ 3 = 2n ÷ 2 ⇒1536 ÷ 3 × 2 = 2n ⇒1024 = 2n ⇒210 = 2n ∴ n = 10 Sum of a G.P. series is...
In a GP, the ratio of the sum of the first three terms is to first six terms is 125 : 152. Find the common ratio.
Answer : Sum of a G.P. series is represented by the formula, when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and...
Evaluate : NOTE: In an expression like this n represents the upper limit, 1 represents the lower limit , x is the variable expression which we are finding out the sum of and i represents the index of summarization.
Find the sum :
Find the sum to n terms of the sequence :
Find the sum of the GP : x(x + y) + x2(x2 + y2) + x3(x3 + y3) + …. To n terms
Answer : The given expression can be written as = (x2+ xy) + (x4 + x2y2 ) + (x 6 + x3y3 ) + …. To n terms = (x2 + x4 + x6 + … to n terms ) + ( xy + x2y2 + x3y3 + … to n terms )
Find the sum of the GP : x3 + x5 + x7 + …. To n terms
Find the sum of the GP : 1 – a + a2 – a3 + …to n terms ( a ≠ 1)
B. Find the sum of the GP :
Find the sum of the GP :
Answer : Sum of a G.P. series is represented by the formula, , when r>1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’...
Find the sum of the GP :
Answer : Sum of a G.P. series is represented by the formula, when |r|<1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio...
Find the sum of the GP : ???? − ????/ ???? + ????/ ???? = ????/ ???? +. .. to 9 terms
Answer : Sum of a G.P. series is represented by the formula, when |r|<1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio...
Find the sum of the GP : 0.15 + 0.015 + 0.0015 + …. To 6 terms
Answer : Sum of a G.P. series is represented by the formula, when |r|<1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio...