# Which Term of the Ap 3, 15, 27, 39, .... Will Be 120 More than Its 21st Term? - Mathematics

Sum

Which term of the AP 3, 15, 27, 39, .... will be 120 more than its 21st term?

#### Solution

In the given problem, let us first find the 21st term of the given A.P.
A.P. is 3, 15, 27, 39 …
Here,
First term (a) = 3
Common difference of the A.P. (d) = 15 - 3 = 12
Now, as we know, an = a + (n -1)d
So, for 21st term (n = 21),
a21 = 3 + (21 - 1)(12)
= 3 +20(12)
= 3 + 240
= 243

Let us take the term which is 120 more than the 21st term as an.

an = 120 + a21
So, an = 120 + 243
an = 363

Also, an = a +(n - 1)d
363 = 3 + (n -1)12
363 = 3 + 12n - 12
363 = -9 = 12n

363+ 9 = 12n

Further simplifying, we get
372 = 12n

"n" = (370)/(12)

n = 31

Therefore, the 31st term of the given A.P. is 120 more than the 21st term.

Concept: Algebraic Conditions for Number of Solutions
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