Question

Find the first term and the common difference of an A.P whose eleventh term is 38 and the sixteenth term is 73​

Answer 1

Given :-

• 11th term of AP=38

• 16th term of AP=73

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To find :-

• Common difference of AP (d)

• First term of AP (a)

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Solution :-

11th term of AP can also be written as:

⇒ a+10d=38---(1.)

Here a defines first term and d refers to Common difference.

16th term of AP can also be written as:

⇒ a+15d=73---(2.)

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Subtract equation (1.) from (2.)

⇒ a+15d-(a+10d)=73-38

⇒ a+15d-a-10d=35

⇒ 10d=35

⇒ d=35/10

$\large\boxed{\sf d=3.5}$

Now substitute this value in equation (1.)

⇒ a+10d=38

⇒ a+10(3.5)=38

⇒ a+35=38

⇒ a=38-35

$\large\boxed{\sf{a=3}}$

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So the first term and Common difference of AP are:-

• First term=a=3

• Common difference=d=3.5

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