Question

Which term of the arithmetic progression 8, 14, 20, 26, ... will be 72 more than its 41st term.

Answer 1

Answer:

53rd term of the A.P   8, 14, 20, 26, ... will be 72 more than its 41st term.

Step-by-step explanation:

Given :  

8, 14, 20, 26, ..

first term , a = 8 , common difference , d = 14 - 8 = 6

nth term = 72 + a41

a + (n -1)d = 72 + a41

[nth term = a + (n -1)d]

8 + (n - 1) 6 = 72 + a + (41 - 1) d

8 + 6n - 6 = 72 + 8 + 40 ×  6

2 + 6n  = 72 + 8 + 240

2 + 6n   = 80 + 240

2 + 6n  = 320

6n = 320 - 2

6n = 318

n = 318/6

n = 53

Hence, 53rd term of the A.P   8, 14, 20, 26, ... will be 72 more than its 41st term.

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Answer 2

Answer: 53rd term

Step-by-step explanation:

Given A.P : 8, 14, 20, 26..

a = 8 ( first term )

d = 14 - 8 = 6 ( common difference )

nth term = 72 + a41

» a + (n -1)d = 72 + a41

» 8 + (n - 1) 6 = 72 + a + (41 - 1) d

» 8 + 6n - 6 = 72 + 8 + 40 ×  6

» 2 + 6n  = 72 + 8 + 240

» 2 + 6n   = 80 + 240

» 2 + 6n  = 320

» 6n = 318

» n = 318/6

» n = 53

Thus, 53rd term of the A.P 8, 14, 20, 26... will be 72 more than its 41st term.