Question

1. if the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

Answer 1

Hope it will help you.....

Answer 2

The required ratio of the first term to the common difference is 2:3.

Step-by-step explanation:

Consider the provided information.

The formula to calculate the nth term of an AP is: $a_n=a+(n-1)d$

Where a is the first term, d is the difference n is the number of term and aₙ is the nth term.

It is given that the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms,

This can be written as:

$[a+(7-1)d]^2=[a+(3-1)d][a+(17-1)d]$

$(a+6d)^2=(a+2d)(a+16d)$

$a^2+36d^2+12ad=a^2+16ad+2ad+32d^2$

$36d^2-32d^2=18ad-12ad$

$4d^2=6ad$

$4d=6a$

$\dfrac{a}{d}=\dfrac{4}{6}=\dfrac{2}{3}$

Hence, the required ratio of the first term to the common difference is 2:3.

#Learn more

THE SUM OF FIRST 20 TERMS OF A G.P. IS 244 TIMES THE SUM OF ITS FIRST 10 TERMS. the comman ratio is?

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