Question

The sum of the 4 consecutive term of GP is 1296.Find the 1st term?​

Answer 1

QUESTION:

• The product of the 4 consecutive term of GP is 1296.Find the 1st term?

ANSWER:

Given:

• Product of 4 consecutive terms of a GP = 1296

To Find:

• First term of the GP

Solution:

$\text{Let the consecutive terms be \dfrac{a}{r^3}, \dfrac{a}{r}, ar, ar^3 .}\\\\\text{We chose these terms so that,}\\\\\text{The common ratio (r) gets cancelled when we multiply the terms.}\\\\\text{This leaves us with the 1st terms(a) only.}\\\\\text{We are given that,}\\\\:\longrightarrow\dfrac{a}{r^3}\times\dfrac{a}{r}\times ar\times ar^3=1296\\\\:\implies\dfrac{a}{r^3\!\!\!\!\!/}\times\dfrac{a}{r\!\!\!/}\times ar\!\!\!/\times ar^3\!\!\!\!\!\!/=1296\\\\:\implies a\times a\times a\times a=1296\\\\:\implies a^4=1296$

$\text{Now,}\\\\:\implies a=\sqrt[4]{1296}\\\\\bf{:\implies a=\pm6}\\\\\text{\bf{The first term is \pm 6}}$

Learn More:

• a_n = ar^(n-1)
• S_n = (ar^n - 1)/(r-1)