Question

an AP consists of 60 terms of which 3rd term is 7 and the last term is 178 find the 19th term​

Answer 1

Given :-

• Number of terms in AP = 60
• 3rd term of AP = 7
• last term of AP = 178

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To find :-

• 19th term of AP

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Solution :-

In order to find the 19th term of AP, firstly we have to find the common difference and first term of the AP.

3rd term of AP = 7 [Given]

⇝ a3 = 7

⇝ a + 2d = 7 - - - - Eqn(1)

last term of AP = 178 [Given]

⇝ a60 = 178

⇝ a + 59d = 178 - - - - Eqn(2)

Eqn(2) - Eqn(1)

⇝ a + 59d - (a + 2d) = 178 - 7

⇝ a + 59d - a - 2d = 171

⇝ 57d = 171

⇝ d = 171 / 57

⇝ d = 3

Substitute this value of d in Eqn(1) :-

⇝ a + 2d = 7

⇝ a + 2(3) = 7

⇝ a + 6 = 7

⇝ a = 7 - 6

⇝ a = 1

Now we have formula to find nth term of AP :-

⇝ an = a + ( n - 1 ) d

Substitute value of a = 1 , d = 3 and n = 19 for 19th term

⇝ a19 = 1 + ( 19 - 1 ) ( 3 )

⇝ a19 = 1 + ( 18 ) ( 3 )

⇝ a19 = 1 + 54

⇝ a19 = 55

So the required 19th term of AP is 55.

More :-

• To find common difference, we can subtract succeeding term from it's preceding term.

• nth term can also be expressed as Tn.

• Both a1 and a means same i.e. first term.

Answer 2

Amswer is 53.

Thank You...