Question

The 7th term of an ap is 34 and the 15th term is 74. find its 40th term.​

Answer 1

EXPLANATION.

The 7th term of an ap = 34.

The 15th term of an ap = 74.

As we know that,

General term of an ap.

⇒ Tₙ = a + (n - 1)d.

Using this formula in the equation, we get.

The 7th term of an ap = 34.

⇒ T₇ = a + (7 - 1)d.

⇒ T₇ = a + 6d.

⇒ a + 6d = 34. - - - - - (1).

The 15th term of an ap = 74.

⇒ T₁₅ = a + (15 - 1)d.

⇒ T₁₅ = a + 14d.

⇒ a + 14d = 74. - - - - - (2).

From equation (1) and (2).

Subtract both the equation, we get.

⇒ a + 6d = 34. - - - - - (1).

⇒ a + 14d = 74. - - - - - (2).

⇒ -  -           -

We get,

⇒ - 8d = - 40.

⇒ 8d = 40.

⇒ d = 5.

Put the value of d = 5 in equation (1), we get.

⇒ a + 6d = 34.

⇒ a + 6(5) = 34.

⇒ a + 30 = 34.

⇒ a = 34 - 30.

⇒ a = 4.

First term = a = 4.

Common difference = d = b - a = 5.

To find : 40th term of an ap.

⇒ T₄₀ = a + (40 - 1)d.

⇒ T₄₀ = a + 39d.

Put the values in the equation, we get.

⇒ T₄₀ = 4 + 39(5).

⇒ T₄₀ = 4 + 195.

⇒ T₄₀ = 199.

Answer 2

Answer:

The $40^{th}$ term of the AP is  $a_{40} =199$ .

Step-by-step explanation:

This question can be solved by using the general term of AP.

The $n^{th}$ term of an AP is   $a_{n} =a+(n-1)d$.

Given $7^{th}$ term is $34$, that is   $a_{7} =a+6d=34$ . . . . (1)

and $15^{th}$ term is $74$, that is     $a_{15} =a+14d=74$ . . . . (2)

Solving (1) and (2) , to find the value of $d$. and then apply it to any one of these equation, we can find the value of $a$,  and hence we can write the $n ^{th}$ term of the AP, after that substitute each values to find the $40^{th}$ term.

So, (2)-(1) ⇒

                   $a+14d=74\ -\\\\a+6d=34$                                                                                                                                ⇒  

                         $8d=40\\\\d=40/8=5$

Applying $d=5$  in  (1),  

                         $a+6(5)=34\\\\a=34-30=4$

Therefore $a_{n} =a+(n-1)d=4+(n-1)5$

We are asked to find the $40^{th}$ term

                 $a_{40} =a+39d=4+39(5)$

                       $=199$

Hence the answer

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