How many terms are there in the G.P. 3, 6, 12, 24, …, 384?

Given data

• Geometric progression (G.P.): 3, 6, 12, 24, …, 384
• First term a = 3, common ratio r = 2, last term = 384

Concept / Approach

• n-th term of a G.P.: T_n = a · r^{n−1}
• Set T_n = 384 and solve for n.

Step-by-step calculation

384 = 3 · 2^{n−1}⇒ 2^{n−1} = 384 ÷ 3 = 128 = 2^7⇒ n − 1 = 7 ⇒ n = 8

Verification

Terms: 3,6,12,24,48,96,192,384 — there are 8 terms.

Common pitfalls

• Mistaking r as 3 (it is 2).
• Using arithmetic progression formula (not applicable).

Final Answer

Number of terms = 8.