Question

which term of the A.P 20, 17, 14 ,11....is -16?​

Answer 1

Answer :

$n = 13$

Step-by-step explanation :

Given A.P is :20,17,14,11,..............,-16

Let the first term be a, common difference is d and n is the number of terms.

We know that nth term of an Arithmetic progression is in the form ;

Tn = a + (n-1)d

Now,

→d = 17 - 20 = - 3

And,

→a = 20.

So according to the question,

Tn = a + (n-1)d

→ -16 = 20 + (n-1)×-3

→ -16 = 20 + (-3n+3)

→ -16 = 20 - 3n +3

→ -16 - 20 - 3 = - 3n

→ -39 = - 3n

→ $\frac{39}{3} = 13 = n$

Therefore, the 13th term of the A.P is - 16.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Which\:term\:is\:-16=13th\:term}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P = 20,17,14,11.... \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Which \: term \: is \: - 16 =?$

• According to given question :

$\tt \circ \: First \: term(a) = 20 \\ \\ \tt \circ \: Common \: difference(d) = - 3 \\ \\ \tt \circ \: Last \: term( a_{n}) = - 16 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1)d \\ \\ \tt: \implies - 16 = 20 + (n - 1 )\times - 3 \\ \\ \tt: \implies - 16 - 20 = (n - 1) \times - 3 \\ \\ \tt: \implies - 36 = (n - 1) \times - 3 \\ \\ \tt: \implies \frac{ - 36}{ -3} = n - 1 \\ \\ \tt: \implies 12 = n - 1 \\ \\ \tt: \implies n = 12 + 1 \\ \\ \green{\tt: \implies n = 13th \: term } \\ \\ \green{\tt \therefore - 16 \: is \: 13th \: term \: of \: this \: A.P}$