Which term of the AP 3, 8, 13, 18, …will be 55 more than its 20th te

1.	Which term of the AP 3, 8, 13, 18, …will be 55 more than its 20th term?
Answer» Given AP is 3, 8, 13, 18,… First term = a = 3 Common difference = d = 8 – 3 = 5 And n = 20 and a₂₀ be the 20^th term, then a₂₀ = a + (n – 1)d = 3 + (20 – 1) 5 = 3 + 95 = 98 The required term = 98 + 55 = 153 Now, 153 be the nth term, then a_n = a + (n – 1)d 153 = 3 + (n – 1) x 5 153 – 3 = 5(n – 1) 150 = 5(n – 1) n – 1 = 30 n = 31 Required term will be 31st term.

Which term of the AP 3, 8, 13, 18, …will be 55 more than its 20th term?

Answer»

Given AP is 3, 8, 13, 18,…

First term = a = 3

Common difference = d = 8 – 3 = 5

And n = 20 and a₂₀ be the 20^th term, then

a₂₀ = a + (n – 1)d

= 3 + (20 – 1) 5

= 3 + 95

= 98

The required term = 98 + 55 = 153

Now, 153 be the nth term, then

a_n = a + (n – 1)d

153 = 3 + (n – 1) x 5

153 – 3 = 5(n – 1)

150 = 5(n – 1)

n – 1 = 30

n = 31

Required term will be 31st term.