Question

Which term of the ap 3,14 ,25,36 is 99 more than its 25th term

Answer 1

an = 99 + a25

=99 + a + 24d

=99 + 3 +24 * 12

= 390

Answer 2

34th term

Explanation:

the nth term of an AP is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and d = a₂ - a₁ = 14 - 3 = 11 , then

`a_(n)` = 3 + 11(n - 1) = 3 + 11n - 11 = 11n - 8

substitute n = 25 into the rule to find a₂₅ , that is

a₂₅ = 11(25) - 8 = 275 - 8 = 267

then 99 more than this is 267 + 99 = 366

equate 11n - 8 to 366 and solve for n

11n - 8 = 366 ( add 8 to both sides )

11n = 374 ( divide both sides by 11 )

n = 34

then the 34th term is 99 more than the 25th term