Question

the first fourth trem of an A.P are 1,9,a and b. find the 1) vale of a and 2) 15th of A.P​

Answer 1

Answer:

a = 17 ;  b = 25    ;    T₁₅ = 113

Step-by-step explanation:

First term(T₁) = 1

Common difference = a₂ - a₁ = 9 - 1

                                  = 8

Using Tₙ = T₁ + (n - 1)d

⇒ T₃ = T₁ + (3 - 1)d

⇒ a = 1 + (2)(8)

⇒ a = 1 + 16

⇒ a = 17

   Similarly, T₄ = b

⇒ T₄ = T₁ + (4 - 1)d

⇒ b = 1 + (3)(8)

⇒ b = 1 + 24

⇒ b = 25

      Using the same procedure for T₁₅

⇒ T₁₅ = T₁ + (15 - 1)d

         = 1 + (14)(8)

         = 1 + 112

         = 113

Answer 2

Given :

First term $\sf a_1 = 1$

Second term $\sf a_2 = 9$

Third term $\sf a_3 = a$

Fourth term $\sf a_4 = b$

To Find :

(1) Find the value of a and b

(2) $\sf A_{15}$ term

Explanation :

____________________

(1)

$\longrightarrow$In this question We have already $\sf a_1$ = 1 and $\sf a_2$ = 9

$\longrightarrow$ So, For common difference = $\sf a_2 - a_1$ = 9 - 1 = 8

$\longrightarrow$For a

• $\sf a = a_3$

$\longrightarrow$And also we had find out that d = 8

So,

• $\sf d = a_3 - a_2$

• $\sf 8 = a - 9$

• $\sf 8 + 9 = a$

• $\sf \underline{\boxed{a = 17}}$

$\longrightarrow$Now, again for b

• $\sf b = a_4$

$\longrightarrow$And also we had find out that d = 8

So,

• $\sf d = a_4 - a_3$

• $\sf 8 = b - 17$

• $\sf 8 + 17 = b$

• $\sf \underline{\boxed{b = 25}}$

____________________

(2) Now, we have already $\sf a_1 = 1$

n = 15 and d = 8

• $\sf a_{15} = a_1 + (n - 1 ) d$

• $\sf a_{15} = 1 + (15 - 1 ) (8)$

• $\sf a_{15} = 1 + (14)(8)$

• $\sf a_{15} = 1 + 112$

• $\sf \underline{\boxed{a_{15} = 113 }}$

____________________

I hope it helps you ❤️✔️