Question

Find the nth term and the 12th term of the list of number : 5,2,-1, -4,...​

Answer 1

Answer:

a=5

d=2-5= -3

an=a+(n-1)d

n=n,12

a12= a+(12-1)d

a12= 5+11× -3

a12= 55+(-3)

a12 =52

an = 5+( n-1)× -3

an= 5+(-3n) +3

an= 8 -3n

Answer 2

★GIVEN★

AP = 5, 2, -1, -4

★To Find★

Find the nth term and the 12th term of the list.

★SOLUTION★

We know the formula to find the nth term is,

$\large{\underline{\boxed{\sf{a_{n}=a+(n-1)d}}}}$

where,

• $\small{\bf{a_{n}\:is\:the\:nth\:term}}$
• a is the first term
• n is the nth term
• d is the common difference

Now,

• a is 5
• d = (-1) -2 = -3

$\large\implies{\sf{a_{n}=a+(n-1)d}}$

Putting the values,

$\large\implies{\sf{a_{n}=5+(n-1)(-3)}}$

Multiplying (n-1) with (-3),

$\large\implies{\sf{a_{n}=5+(-3n)-(-3)}}$

$\large\implies{\sf{a_{n}=5-3n+3}}$

$\large\implies{\sf{a_{n}=8-3n}}$

$\large{\underline{\boxed{\therefore{\sf{a_{n}=8-3n.}}}}}$

• ★Now the 12th term of the list★

Putting n=12 in 8-3n,

$\large\implies{\sf{a_{12}=8-(3\times12)}}$

$\large\implies{\sf{a_{12}=8-36}}$

$\large\implies{\sf{a_{12}=-28}}$

$\large{\underline{\boxed{\therefore{\sf{a_{12}=-28.}}}}}$

$\large{\red{\underline{\boxed{\therefore{\bf{1))\:nth\:term\:is\:8-3n.}}}}}}$

$\large{\red{\underline{\boxed{\therefore{\bf{2))\:12th\:term\:is\:-28.}}}}}}$