Question

If 6th and 17th term of A. P. are 19 and 41 respectively, then find the 40th term

Please answer this question fast

Answer 1

Answer:

40th term of the A.P. is 87.

Step-by-step explanation:

Given :-

• 6th and 17th term of an A.P. are 19 and 41.

To find :-

• The 40th term.

Solution :-

Formula used :

${\boxed{\sf{T_n=a+(n-1)d}}}$

• a = first term
• d = Common difference

★$\sf{T_6=a+(6-1)d}$

$\to\sf{T_6=a+5d}$

And,

★$\sf{T_{17}=a+(17-1)d}$

$\to\sf{T_{17}=a+16d}$

According to the question ,

a+5d = 19..............(I)

a+16d = 41.............(ii)

Now subtract eq(i) from eq(ii).

a+16d -(a+5d) = 41-19

→ a + 16d -a -5d = 22

→ 11d = 22

→ d = 2

Now put d = 2 in equation (I).

a+5d = 19

→ a + 5×2 = 19

→ a +10 = 19

→ a = 19-10

→ a = 9

Now find the 40th term of the A.P.

$\to\sf{T_{40}=a+(40-1)d}$

$\to\sf{T_{40}=9+39\times\:2}$

$\to\sf{T_{40}=87}$

Therefore, the 40th term of the A.P. is 87.

Answer 2

✦ GIVEN :

6th term of A. P.= 19

17th term of A. P. = 41

✦ TO FIND :

the 40th term

✦ FORMULA USED:

Tn = a+(n-1)d

where:-

• Tn= nth term
• n = number of terms
• a = first term
• d = common difference

✦ SOLUTION :

6th term of A. P.= 19

★ By using the formula Tn = a+(n-1)d we can write 6th term as :-

$⟶T6 = a+(6-1)d$

$⟶19= a+5d$

$ㅤㅤㅤㅤㅤ</p><p>∴a = 19 - 5d$

17th term of A. P. = 41

★ By using the formula Tn = a+(n-1)d we can write 17th term as :-

$⟶T17= a+(17-1)d$

$⟶41= a+16d$

$\: \: \: ∴a = 41 - 16d$

★ we got , a = 41-16d and a = 19-5d

therefore :-

$⟶</strong><strong>41-16d</strong><strong>=</strong><strong>19-5d</strong><strong>$

$⟶-16d</strong><strong>+</strong><strong>5d</strong><strong>=19</strong><strong>-</strong><strong>4</strong><strong>1</strong><strong>$

$⟶-1</strong><strong>1</strong><strong>d=</strong><strong> </strong><strong>-</strong><strong>2</strong><strong>2</strong><strong>$

$⟶d= -22</strong><strong>/</strong><strong>-</strong><strong>1</strong><strong>1</strong><strong>$

$⟶d= 2$

Therefore, d = 2

★ To find the value of a , put d=2 in a = 19-5d.

⟶a = 19-5(2)

⟶a= 19-10

⟶a=9

★ Now to find the 40th term use the formula => Tn = a+(n-1)d

And put a = 9 , d= 2 and n = 40

⟶T40 = 9+(40-1)2

⟶T40 = 9+(39×2)

⟶T40 = 9+78

⟶T40 = 87

✦ ANSWER :

40th term Of A.P = 87

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✦ Learn more :-

1. Tn = a+(n-1)d

2. Sn = n/2[2a+(n-1)d]

3. Sn = n/2(a+l)

where:-

★ Tn= nth term

★ n = number of terms

★ a = first term

★ d = common difference

★ l = last term

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