Question

The general form of an AP is an=3n+1 then a5 is​

Answer 1

EXPLANATION.

General form of an A.P. = 3n + 1.

As we know that,

⇒ aₙ = 3n + 1.

Put the value of n = 1 in the equation, we get.

⇒ 3(1) + 1.

⇒ 3 + 1 = 4.

Put the value of n = 2 in the equation, we get.

⇒ 3(2) + 1.

⇒ 6 + 1 = 7.

Put the value of n = 3 in the equation, we get.

⇒ 3(3) + 1.

⇒ 9 + 1 = 10.

Put the value of n = 4 in the equation, we get.

⇒ 3(4) + 1.

⇒ 12 + 1 = 13.

Series = 4, 7, 10, 13 . . . . .

First term = a = 4.

Common difference = d = b - a = c - b.

Common difference = d = 7 - 4 = 3.

To find :

T₅ term.

As we know that,

⇒ Aₙ = a + (n - 1)d.

⇒ T₅ = a + (5 - 1)d.

⇒ T₅ = a + 4d.

Put the value in the equation, we get.

⇒ T₅ = (4) + 4(3).

⇒ T₅ = 4 + 12.

⇒ T₅ = 16.

                                                                                                                     

MORE INFORMATION.

Supposition of an A.P.

(1) = Three terms as : a - d, a, a + d.

(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.

Answer 2

Answer:

16

Step-by-step explanation:

$\boxed{ \color{yellow} \huge{ \colorbox{gray}{Given :-}}}$

$\: : \implies \: a_n = a + (n - 1)d = 3_n + 1$

Putting n = 1

$\: : \implies \: \boxed{a_1 = 3 \times 1 + = 4}$

Putting n = 2

$\: : \implies a_2 = 3 \times 2 + 1 = 7$

$\: : \implies \: a_2 = a + d = 7$

$\: : \implies \: 4 + d = 7$

$\: : \implies \: \boxed{d = 7 - 4 = 3}$

$a_5 = 4+ (5 - 1)3$

$\: : \implies \: a_5 = 4 + 4 \times 3$

$\: : \implies \: \boxed{a_5 = 16}$