Question

in an A.P the sum of four terms is 52.the product of extremes and the product of means are in the ratio 11:20 find the terms ​

Answer 1

$\text{Let the four terms of the A.P be a-3d,a-d,a+d,a+3d }$

$\textbf{Given:}$

$\text{Their sum is 52 and the product of extremes}$

$\text{and the product of means are in the ratio 11:20}$

$\textbf{To find:}$

$\text{The terms of the A.P}$

$\textbf{Solution:}$

$\text{Sum of the four terms =52}$

$(a-3d)+(a-d)+(a+d)+(a+3d)=52$

$\implies\,4a=52$

$\implies\bf\,a=13$

$\text{Also,}$

$(a-3d)(a+3d):(a-d)(a+d)=11:20$

$(a^2-9d^2):(a^2-d^2)=11:20$

$\dfrac{13^2-9d^2}{13^2-d^2}=\dfrac{11}{20}$

$\dfrac{169-9d^2}{169-d^2}=\dfrac{11}{20}$

$20{\times}169-180d^2=11{\times}169-11d^2$

$20{\times}169-11{\times}169=180d^2-11d^2$

$9{\times}169=169d^2$

$\implies\,d^2=9$

$\implies\,d={\pm}3$

$\text{when d=3}$

$\text{The four terms are}$

$13-9,13-3,13+3,13+9$

$\bf\,4,10,16,22$

$\text{when d=-3}$

$\text{The four terms are}$

$13+9,13+3,13-3,13-9$

$\bf\,22,16,10,4$

$\textbf{Find more:}$

1.The sum of first q terms of an A.P. is 63q – 3q². If its pth term is-60, find the value of p. Also, find the 11th term of this A.P.

https://brainly.in/question/15930752

2.The sum of first m terms of an A.P. is 4 m² - m. If its nth term is 107, find the value of n. Also, find the 21st term of this A.P.

https://brainly.in/question/15930761

3.AP given that the first term (a) = 54, the common difference

(d) = -3 and the nth term (an) = 0, find n and the sum of first n terms (Sn)

of the A.P.​

https://brainly.in/question/15922933