Question

If the first term of an AP is-24 and its 13th term is zero then find it’s common difference

Answer 1

Answer:

The common difference is 2.

Given:

• The first term of an AP is -24.

• $\sf{13^{th}}$ term is zero.

To find:

• Common difference (d).

Solution:

$\boxed{\sf{tn=a+(n-1)d}}$

$\sf{\therefore}$ t13= -24+(13-1)d

$\sf{\therefore}$ 0= -24+12d

$\sf{\therefore}$ 12d=24

$\sf{\therefore{d=\frac{24}{12}}}$

$\sf{\therefore}$ d=2

The common difference is 2.

Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{If \ the \ first \ term \ of \ an \ AP \ is \ -24 \ and }$

$\rm{its \ 13^{th} \ term \ is \ zero \ then \ Find }$

$\rm{it's \ common \ difference}$

_________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm{\blue{\boxed{\red{The \ common \ difference \ is \ 2.}}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{The \ first \ term \ of \ an \ AP \ is \ -24.}$

$\rm{{13^{th} \ term \ is \ zero.}}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Common \ difference \ (d).}$

_________________________________________

$\green{\underline{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}}$

$\rm{We \ are \ given,}$

$\rm{The \ first \ term \ of \ an \ AP \ is \ -24.}$

$\rm{t_1 \ = \ -24}$

$\rm{{13^{th} \ term \ is \ zero.}}$

$\rm{t_13 \ = \ 0}$

$\rm{We \ know,}$

$\rm{\green{\boxed{\orange{t_n=a+(n-1)d}}}}$

$\rm{\therefore{ t_13= -24+(13-1)d}}$

$\rm{\therefore{ 0= -24+12d}}$

$\rm{\therefore{12d=24}}$

$\rm{\therefore{d=\frac{24}{12}}}$

$\rm{\therefore{\red{\boxed{\blue{d=2}}}}}$

$\rm{\blue{\boxed{\red{The \ common \ difference \ is \ 2.}}}}$

________________________________________

$\rm\orange{Hope \ this \ helps \ :))}$