Question

he sum of first n terms of ap is5n^2+3n. if it's mth term is 168, find the value of m​

Answer 1

Answer:

m = 17

Step-by-step explanation:

Given---> Sum of first n terms of AP is ( 5n² + 3n )

and its mth term is 168

To find---> Value of m

Solution---> Let first term of AP be a and common difference of AP be d .

Now, ATQ,

Sₙ = 5n² + 3n

Putting n = 1 in it we get sum of one term only which is equal to first term so,

S₁ = 5 ( 1 )² + 3 ( 1 )

= 5 ( 1 ) + 3

= 5 + 3

= 8

So first term of AP = S₁

a = 8

Now putting n = 2 in Sₙ , we get,

S₂ = 5 ( 2 )² + 3 ( 2 )

= 5 ( 4 ) + 6

= 20 + 6

= 26

S₂ means Sum of two terns, so,

S₂ = a₁ + a₂ = 26

8 + a₂ = 26

a₂ = 26 - 8

a ₂ = 18

Now , Common difference = a₂ - a₁

= 18 - 8

= 10

ATQ, mth term = 168

aₘ = 168 , a = 8 , d = 10 , m = ?

Formula of nth term of AP is,

aₙ = a + ( n - 1 ) d

=> aₘ = 8 + ( m - 1 ) 10

=> 168 = 8 + 10m - 10

=> 168 - 8 + 10 = 10 m

=> 160 + 10 = 10 m

=> 170 = 10 m

=> m = 170 / 10

=> m = 17

#Answerwithquality&BAL

Answer 2

$<font color =“orange”>$

${ \huge \bf{ \mid{ \overline{ \underline{Answer}}} \mid}}$

m=17

#answerwithquality #bal