Question

which term of the AP 5,9,13,17, •••• is 81?​

Answer 1

Answer:

★ ANSWER :

The 20th term of Arithmetic Progression is 81.

Step-by-step explanation:

★ QUESTION :

Which term of the AP 5 , 9 , 13 , 17 ........... is 81 ?

★ CONCEPT USED :

Arithmetic Progression (AP) = a1 , a2 , a3 ...... an

Common Difference (d) = a2 - a1

nth Term (an) = a + (n - 1)d

Sum of nth Term (Sn) = n/2 (a + an)

Sum of nth Term (Sn) = n/2 + { 2a + (n - 1)d }

★ SOLUTION :

Let us assume that the nth term of the AP be 81.

Arithmetic Progression (AP) = 5 , 9 , 13 , 17 ........... 81

Common Difference (d) = a2 - a1

d = 9 - 5

d = 4

nth Term (an) = a + (n - 1)d

81 = 5 + (n - 1)4

→ 81 - 5 = (n - 1)4

→ 76 = (n - 1)4

→ 76/4 = n - 1

→ 19 = n - 1

→ 19 + 1 = n

→ 20 = n

→ n = 20

Therefore , the 20th term of Arithmetic Progression is 81.

★ ANSWER :

The 20th term of Arithmetic Progression is 81.

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