Question

Find the 12th term the AP 2, 7, 12, 17,​

Answer 1

EXPLANATION.

Series = 2, 7, 12, 17,,,,,

As we know that,

First term = a = 2.

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

Common difference = d = 7 - 2 = 12 - 7.

Common difference = d = 5.

General term of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₁₂ = a + (12 - 1)d.

⇒ T₁₂ = a + 11d.

⇒ T₁₂ = 2 + 11(5).

⇒ T₁₂ = 2 + 55.

⇒ T₁₂ = 57.

                                                                                                                         

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:

$\sf{55}$

Step-by-step explanation:

Question:

$\underline{\tt{Find\:the\: 12th \:term \:of\:the\: AP\: 2, 7, 12, 17}}$

• a=2
• d=5

Solution:

$\begin{gathered} \\ \\ \: \: \clubsuit \: \sf{a_{12}= a+11d} \\ \\ \: \: \implies \: \sf{a_{12}= 2+11 \: \times \:5} \\ \\ \implies \: \sf{2+55} \\ \\ \: \implies \: \sf{57} \\ \\ \end{gathered}$