Question

25th term of an arithmetic progression is 75 and difference of 25th and 24th term is 5 then what is the 5th term of that series

Answer 1

Answer:-25

Step-by-step explanation:a+24x5=75

a=-45

a+4d=-45+20=-25=5th term

Answer 2

$\huge \bold{For \: an \: AP}$

Arithmetic progression is the series in which the values comes after a common interval which is previous term subtracted from next term.

$\mathsf{t_n= a + (n -1)d}$

where

a = first term

d = common difference

n= number of terms

$\huge \bold{Given}$

$\mathsf{t_{25}= 75}$

$\mathsf{a + 24 d = 75}$....(1)

$\mathsf{t_{25} - t_{24} = 5}$

Since, we know that the next term when is subracted from previous term its common difference d. Which means common difference d = 5.

On placing value of d is equation 1.

$\mathsf{a + 24 d = 75}$

$\mathsf{a + 24 \times 5= 75}$

$\mathsf{a + 120= 75}$

$\mathsf{a = 75 - 120}$

$\huge \boxed{\mathsf{a =-45}}$

So, 5th term will be

$\mathsf{t_5 = a + (5-1)d}$

$\mathsf{t_5 = -45 + 4 \times 5}$

$\huge \boxed{\mathsf{t_5 =-25}}$