Question

In an A.P, 3rd term is 18 and 17th term is 60 then the 20th term is

Answer 1

Required Answer:-

GiveN:-

• 3rd term (a3) = 18
• 17th term (a17) = 60

By using nth term formula,

✪ $\underline{ \boxed{ \rm{a_n = a + (n - 1)d}}}$

We get,

• a3 = a + 2d = 18 ----(1)
• a17 = a + 16d = 60 ----(2)

Subtracting (1) from (2),

➛ a + 16d - (a + 2d) = 60 - 18

➛ a + 16d - a - 2d = 42

➛ 14d = 42

➛ d = 3

Then, a = 18 - 2(3) = 12

Now, finding the 20th term

= a20

= a + 19d

= 12 + 19(3)

= 12 + 57

= 69 (Ans)

Things can be used:

• In Arithmetic progression, nth term formula, sum of n terms formula, choosing the no. of terms etc. are equally important.

• Take care of (n - 1) in the formula. The 3rd term in an AP is a + 2d, not a + 3d.

Answer 2

Given:-

3rd term (a3) = 18

17th term (a17) = 60

To find:-

20th term

Solution:-

• ==Formula used==

nth term formula,

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

NOW,

$\sf {a_3 =a+(3-1)d } \\⇒ \sf {a + 2d = 18 ----(1)}$

$\sf {a_{17} = a+(17-1)d } \\ ⇒\sf{a + 16d = 60 ----(2)}$

Subtracting (1) from (2),

⇒a + 16d - (a + 2d) = 60 - 18

⇒a + 16d - a - 2d = 42

⇒ 14d = 42

⇒ d = 3 [put in (1)]

Then, a = 18 - 2(3) = 12

Now, 20th term will be ,

=$\sf {a_{20}=a+(20-1)d}$

= a + 19d

= 12 + 19(3)

= 12 + 57

= 69