Question

the third term of an a.p. is -11 and the nineth term is -35 , find the nth term of an a.p.

Answer 1

the nth term of the AP is 1-4n
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Answer 2

Information provided with us :

• Third term of an A.P. is -11.
• Nineth term of that A.P. is -35

What we have to calculate :

• nth term of that A.P.

Performing Calculations :

As we know that general or nth term of an A.P. is calculated by the formula.

• tn = a + (n - 1) d

Here in this formula,

• a is first term
• d is common difference
• n is number of terms

According to the question,

Third term of an A.P. is -11.

So by using the formula we gets,

=> -11 = a + (3 - 1) d

=> -11 = a + 2 × d

=> -11 = a + 2d

=> a = -11 - 2d

According to the question,

In the question it is given that nineth term of the A.P. is -35.

So by using the formula we gets,

=> -35 = a + (9 - 1) d

=> -35 = a + (8) d

=> -35 = a + (8) × d

=> -35 = a + 8d

So here we would be substituting the value of a which we got above as (-11 - 2d)

=> -35 = -11 - 2d + 8d

=> -35 = -11 + 6d

=> -35 + 11 = 6d

=> 6d = -24

=> d = - 24/6

=> d = -4

• Therefore, common difference is -4.

★ Finding out first term :

=> a = -11 - 2d

=> a = -11 - 2(-4)

=> a = -11 - 2 × -4

=> a = -11 + 8

=> a = -3

• Therefore, first term of the A.P. is -3.

Finding out nth term of the A.P. :

=> tn = a + (n - 1) d

=> tn = -3 + (n - 1) -4

=> tn = -3 - 4n + 4

=> tn = 1 - 4n

Henceforth,

• nth term of the A.P. is 1 - 4n.

Additional Information :

• Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding term
• Difference between two consecutive terms is called common difference
• Progression means it's a type of sequence in which each term is related to its predecessor and successor.

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