Question

The sum and product of three respective terms in A.P is 15 and 80. Find the terms of
an Arithmetic progression​

Answer 1

$\textbf{Given:}$

$\text{The sum and product of three respective terms in A.P is 15 and 80}$

$\textbf{To find:}$

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

$\textbf{Solution:}$

$\text{Let the three ters of the A.P be}$

$a-d,a,a+d$

$\text{Their sum=15}$

$\implies(a-d)+a+(a+d)=15$

$\implies\,3a=15$

$\implies\bf\,a=5$

$\text{Also, their product is 80}$

$(a-d)a(a+d)=80$

$a(a^2-d^2)=80$

$5(25-d^2)=80$

$25-d^2=16$

$d^2=25-16$

$d^2=9$

$d=\pm\,3$

$\text{when d=3}$

$\text{The numbers are 2,5,8}$

$\text{when d=-3}$

$\text{The numbers are 8,5,82}$

$\textbf{The three terms are}$

$\bf\,2,5,8$

$\textbf{Find more:}$

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.

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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.

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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)

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4.If 8 times the 8th term of an AP is equal to 15 times its 15th term then find the 23rd term.

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5.find the four numbers in ap whose sum is 6 and product of whose extreme is 10 times the product of the two intermediate terms

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