Which term of the AP 5, 15, 25,… will be 130 more than its 31st term

1.	Which term of the AP 5, 15, 25,… will be 130 more than its 31st term?
Answer» AP is 5, 15, 25,… First term = a = 5 Common difference = d = 15 – 5 = 10 Find 31^st term: a₃₁ = a + (n – 1)d = 5 + (31 – 1) 10 = 5 + 30 x 10 = 305 Required term = 305 + 130 = 435 Now, say 435 be the nth term, then a_n = a + (n – 1)d 435 = 5 + (n – 1)10 435 – 5 = (n – 1)10 n – 1 = 43 n = 44 The required term will be 44th term.

Which term of the AP 5, 15, 25,… will be 130 more than its 31st term?

Answer»

AP is 5, 15, 25,…

First term = a = 5

Common difference = d = 15 – 5 = 10

Find 31^st term:

a₃₁ = a + (n – 1)d

= 5 + (31 – 1) 10

= 5 + 30 x 10

= 305

Required term = 305 + 130 = 435

Now, say 435 be the nth term, then

a_n = a + (n – 1)d

435 = 5 + (n – 1)10

435 – 5 = (n – 1)10

n – 1 = 43

n = 44

The required term will be 44th term.