Question

Find the first term, if second, third and fourth terms are 21, 80, 120?

Answer 1

A2 =21

A3=80

A4=120

put two values÷÷

by eleminating mathod÷

a+d=21

a+2d=80

__________

-d=-79

minus is cancelled to minus d= 79

put in any one equation

a+79=21

a=21-79

a=-58

A2 =-58+79

=21

so first term of ap is -58

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$first \: term \: - 58$

Answer 2

Answer:

Given,

second term = 21

third term = 80

fourth term = 120

to find: first term

Explanation:

let first term be x

the first, second, third and fourth term are in proportion. Beimg in proportion means the ratio of first two terms will be equal to the ratio of last two terms. For example:

a : b :: c : d are in proportion then a/b = c/d

Accordingly,

x : 21 :: 80 : 120

$\frac{x}{21} = \frac{80}{120} \\ \frac{x}{21} = \frac{2}{3}$

by cross multiplication,

$x = \frac{2 \times 21}{3} = 14$

x = 14

The first term = 14