Question

If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?​

Answer 1

Solution:-

Given

$\rm : \implies T_2 = 13$

$\rm : \implies T_5 = 25$

To find

$\rm : \implies \: T_7$

Formula

$: \implies \boxed{\rm \: T_n = a + (n - 1)d}$

Now

$: \implies\rm \: a \: + d = 13 \: \: \: \: \: .......(i)$

$: \implies \rm \: a \: + 4d = 25 \: \: \: \: .........(ii)$

Subtract( i )from (ii)

$\rm : \implies a + 4d - (a + d) = 25 - 13$

$\rm : \implies \: \cancel{a} + 4d \: - \cancel{a} - d = 12$

$\rm : \implies 3d = 12$

$\rm : \implies d = \dfrac{12}{3} = 4$

$\rm : \implies d \: = 4$

Now put the value of d on (i) eq

$: \implies\rm \: a \: + d = 13 \: \: \: \: \: .......(i)$

$\rm : \implies a + 4 = 13$

$\rm : \implies a = 13 - 4$

$\rm : \implies a = 9$

Now we get a = 9 and d = 4 , so we have to find

$\rm : \implies T_7 = a + 6d$

$\rm : \implies T_7 = 9 + 6 \times 4$

$\rm : \implies T_7 = 9 + 24$

$\rm : \implies T_7 = 33$

So

$\rm \: \boxed{ \rm \: T_7 = 33}$