Question

in the nth termof an AP is 4n²-1then the 8thterm is​

Answer 1

Step-by-step explanation:

nth term of the AP is (4n - 10).

For n = 1, we have a1 = 4 - 10 = - 6

For n = 2, we have a2 = 8 - 10 = - 2

For n = 3, we have a3 = 12 - 10 = 2

For n = 4, we have a4 = 16 - 10 = 6, and so on.

∴ a4 - a3 = a3 - a2 = a2 - a1 = 4 = constant.

∴ the given progression is an AP.

Hence, (i) Its first term = a = - 6

(ii) common difference = 4

(iii) To find :16th term

∴ a16 = a + (16 - 1)d

⇒ a16 = - 6 + 15 × 4 = 54

∴ 16th term of the given AP is 54.

Answer 2

Step-by-step explanation:

$\because \: t_n = 4 {n}^{2} - 1 \\ \\ \therefore \: t_8 = 4 ({8})^{2} - 1 \\ \\ \therefore \: t_8 = 4 \times 64 - 1 \\ \\ \therefore \: t_8 = 256 - 1\\ \\ \huge \orange{ \boxed{ \therefore \: t_8 = 255}}$

Thus 8th term of given AP is 255.