Question

4. How many terms of the geometric series 1 + 4 + 16 + 64 + ... will make
5461?​

Answer 1

Answer:

$\huge \bold {\mathtt{7}}$

Step-by-step explanation:

See the above attachment for formula. Here r is called geometric ratio or common ratio.

Here r is 4 that is r>1.

Therefore we have to use second formula here.

We have to find no. of terms (n).

So,

In this G.P. •first term (a) = 1, •r = 4 and •Sn = 5461

$Sn = \frac{a({r}^{n} - 1 )}{r - 1}$

$5461 = \frac{1( {4}^{n} - 1) }{4 - 1}$

$5461 = \frac{({4}^{n} - 1)}{3}$

${4}^{n} - 1 = 5461 \times 3$

${4}^{n} = 16383 + 1$

${4}^{n} = 16384$

Therefore,

$n = 7$