Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsSequences and SeriesActual

The sum of first three terms of a geometric progression is 16 and the sum of next three terms is 128 . The sum to n terms of the geometric progression is

Options

  1. A8 3 (3^n-1 )
  2. B8 3 (2^n-1 )
  3. C16 7 (3^n-1 )
  4. D16 7 (2^n-1 )

Correct answer

D. 16 7 (2^n-1 )

Step-by-step solution

Let the first term be a and common ratio be r . a(1+r+r^2) = 16 ... (1) ar^3(1+r+r^2) = 128 ... (2) Dividing (2) by (1): r^3 = 8 r = 2 Substituting in (1): a(1+2+4) = 16 a = 16 7 S_n = a(r^n-1) r-1 = 16 7 (2^n-1) 1 = 16 7 (2^n-1)

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Every term of a geometric progression is positive , and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is: 2026If k is the arithmetic mean of two given quantities and p, q are the geometric means between the same two quantities, then p^3 + q^3 is: 2026Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 2 2026The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14. Find the numbers. 2026Let a₁, a₂, a₃, be a geometric progression of positive integers such that a₁ = 3 and a_ n+2 - 2a_n = a_ n+1 for all positive integers n . What is the value of a₁ + a₂ + a₃ + a₄ + a 2026The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is 2026If we insert two numbers between 2 and 4 so that the resulting sequence is in G.P, then the inserted numbers in the order are 2026If S _ n =1^3+2^3+ . .+ n ^3 and T _ n =1+2+ . .+ n , then 2025 Full Sequences and Series list All COMEDK PYQs