Question

sum of nth term of AP whose 7th term is 30 and 13th term 54

Answer 1

Hey there !!

Given :-

→ a₇ = 30.

→ a₁₃ = 54.

To find :-

→ Sn.

Solution :-

WE have,

→ a₇ = 30.

⇒ a + 6d = 30......(1).

And,

→ a₁₃ = 54.

⇒ a + 12d = 54.

On substracting equation (1) and (2), we get

a + 6d = 30.

a + 12d = 54.

-   -          -

__________

⇒ -6d = -24.

⇒ d = 4.

Put the value of d in equation (1), we get

⇒ a + 6d = 30.

⇒ a + 6 × 4 = 30.

⇒ a = 30 - 24 .

⇒ a = 6.

Now,

⇒ Sn = n/2{ 2a + ( n - 1 ) d }.

⇒ Sn = n/2 { 2 × 6 + ( n - 1 )4 }.

⇒ Sn = n/2{ 12 + 4n - 4 }.

⇒ Sn = ( 8n + 4n² )/2 .

⇒ Sn = 2( 4n + 2n² )/2 .

⇒ Sn = 2n² + 4n.

Hence, it is solved,

THANKS

#BeBrainly.

Answer 2

a7=30 a13=54

a+6d=30 a+12d=54

a=30-6d. a=54-12d

30-6d=54-12d

=30-54=-12d+6d

=-24=-6d

=d=-24-6

=d=4

a=30-60x4

30-24

a=6

sn=n/2(2a+(n-1)d)

sn=n/2(2x6+(n-1)x4)

=n/2(12+4n-4)

=(8n+4n'2)/2

=2(4n+2n'2)/2

=sn=2n'2+4n.