Question

Can someone help me with this?​

Answer 1

Its a GP given by 2+6+18

• First term=a=2

Common ratio=r=

Now

• Cancel 2

Answer 2

Let 'a' be the first term, 'r' be the common ratio and 'n' be the number of terms

Series = 2+6+18.......= 2+2•3¹+ 2•3².......= 728

Now,

`Sum = \frac{a( {r}^(n) - 1) }{(r - 1)} \\`

So,

`\frac{a( {r}^(n) - 1)}{(r - 1)} = 728 \\ \frac{2( {3}^(n) - 1) }{(3 - 1)} = 728 \\ \frac{2( {3}^(n) - 1) }{2} = 728 \\ {3}^(n) - 1 = 728 \\ {3}^(n)=728+1\\ {3}^(n) = 729 \\ {3}^(n) = {3}^(6) \\ \boxed{ n = 6}`

Therefore, number of terms is 6

• 6 is the right answer.