Question

solve this step by step.​

Answer 1

Step-by-step explanation:

GIVEN :

sum of GP series (1,3,9,....,) is 364

TO FIND:

no of terms in the series

SOLUTION:

here the ratio between second term to fist term is 3:1 also ratio of third term to second term is 3:1

so it have common ratio as 3

so it is a GP (geometric progression)

let the number of terms be 'n'

so the formula to evaluate sum of GP of finite series is

$s{n} = \frac{a1(1 - {r}^{n}) }{1 - r} \: \: \: \\ where \: r \: is \: not \: equal \: to \: 1$

here a1=first term

r=common ratio

Sn=sum upto n terms

so

$sn = \frac{1(1 - {3}^{n}) }{1 - 3} = 364$

so

1-3^n=364×(-2)

1-3^n=-728

so,

${3}^{n} = 729$

we know that 729=3^6

${3}^{n} = {3}^{6}$

=>

$\huge \boxed{n = 6}$

so there are 6 terms in the GP

Answer 2

Answer:

here's your Answer vicky