Question

if 7 times seventh term of an A.P is equal to 11 times eleventh term , then it's eighteenth term will be
7
11
18
0​

Answer 1

EXPLANATION.

Nth term of an Ap

=> An = a + ( n - 1 ) d

To find the 18th term.

7 times the 7th term of an Ap us equal to

11 times the 11th term of an Ap

=> 7 ( a + 6d ) = 11 ( a + 10d )

=> 7a + 42d = 11a + 110d

=> -4a = 110d - 42d

=> -4a = 68d

=> a = -17d

18th term of an Ap

=> a + 17d

=> -17d + 17d

=> 0

Therefore,

option [ D ] is correct.

Some related formula.

1) = Nth term of an Ap

=> An = a + ( n - 1 ) d

2) = sum of Nth term of an Ap

=> Sn = n/2 ( 2a + ( n - 1 ) d)

Answer 2

Given:-

⠀⠀

if 7 times seventh term of an A.P is equal to 11 times eleventh term.

⠀⠀

To Find:-

⠀⠀

Then it's eighteenth term will be

⠀⠀

1. 7

2. 11

3. 18

4. 0

⠀⠀

STEP BY STEP EXPLANATION:-

⠀⠀

$\bf \implies7(a + (n - 1)d) = 11(a + n - 1)d$

⠀⠀

$\bf \implies7(a + bd) = 11(a + + (od)$

⠀⠀

$\bf \implies7a + 42d = 11a + 11od$

⠀⠀

$\bf \implies \cancel{ - 4a} = 68d$

⠀⠀

$\bf \implies a =2 - 17d$

⠀⠀

$</p><p> \bf \implies a_18 \: it \: is \: also \: down = a + 17d$

⠀⠀

$\bf \implies \cancel{ - 17d} + \cancel{17 d}$

⠀⠀

$\bf \implies 0$