Question

if third term and fifth term of an A.P. are 13 and 25 respectively, find its 7th term​

Answer 1

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Answer 2

SOLUTION

GIVEN

The third term and fifth term of an A.P. are 13 and 25 respectively

TO DETERMINE

The 7 th term

FORMULA TO BE IMPLEMENTED

The ${n}^{th}$term of an Arithmetic progression is

$= a \: + (n - 1)d$

Where First term = a

Common Difference = d

EVALUATION

Let first term = a and common difference = d

Third term = a + 2d

Fifth term = a + 4d

So by the given condition

a + 2d = 13 - - - - - (1)

a + 4d = 25 - - - - - (2)

Equation 2 - Equation 1 gives

2d = 12

$\displaystyle \sf{ \implies \: d = 6}$

From Equation 1 we get

a = 13 - ( 2 × 6 ) = 13 - 12 = 1

Hence 7 th term

= a + 6d

= 1 + ( 6 × 6 )

= 1 + 36

= 37

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