Question

Which term of the AP : 3,8,13,18,.... is 78?

Answer 1

$\bold{We \: \: know , \: \: \: a_{n} \: = a + (n - 1)d}$





d is not given, so

As we know, Common difference = any term - previous term to that term





In question, common difference = 8 - 3 = 5


Hence,


$\bold{78 = 3 + (n - 1)5} \\ \\ = > 78 - 3 = (n - 1)5 \\ \\ = > 75 = (n - 1)5 \\ \\ = > \frac{75}{5} = n \: - 1 \\ \\ = > 15 = n \: - 1 \\ \\ = > 16 = n$






Hence, 16th term of the A.P is 78

Answer 2

Hey there !

Solution:

Formula to be used:

aₓ = a + ( x - 1 ) d

Here a represents the first term, x represents the number of terms and d represents the common difference.

Given information:

• a = 3
• d = 5
• aₓ = 78
• x = ?

Substituting in the formula we get,

78 = 3 + ( x - 1 ) 5

=> 78 - 3 = 5 ( x - 1 )

=> 75 = 5 ( x - 1 )

=> 75 / 5 = ( x - 1 )

=> 15 = x - 1

=> x = 15 + 1 = 16

Hence the 16th term of the AP is 78.

Hope my answer helped !