Correct Answer - Option 4 : 16380

**Given:**

G.P. Series: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

**Formula Used:**

T_{n} = ar^{(n-1)}

S_{n} = a(r^{n}-1)/(n-1)

**Calculation:**

GP Series: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

T_{n} = ar^{n-1}

⇒ 8192 = 4 × (2)^{n-1}

⇒ 2048 = 2^{(n-1)}

Therefore,

⇒ 2^{11 }= 2^{n-1}

⇒ (n – 1) = 11

⇒ n = 12

Sum of series (S) = a(rn- 1)/(n - 1)

⇒ S = 4 × (2^{12} - 1)/ (2 - 1)

⇒ S = 4 × (4096 - 1) = 4 × 4095

∴ S = 16380