Question

If the third term of an AP is 12 and 16th term is 77, find the AP.

Answer 1

let the first term be a
and common difference be d
a+2d=12
a=12-2d---(1)
a+15d=77
from (1)
12-2d+15d=77
13d=65
d=5
a=12-(2×5)
a=2
hence AP is 2,7,12,17....

Answer 2

Question:-

➡ If the third term of an AP is 12 and the 16th term is 77, find the AP

Answer:-

➡ The given AP will be,

2 7 12 17 22....

Solution:-

Given that,

➡ 3rd term of AP is 12.

➡ 16th term of AP is 77

Let us assume that, first term of the AP is a and the common difference be d.

So,

3rd term of the AP = a + (3-1)d

➡ 3rd term = a + 2d

➡ a + 2d = 12 ......... (i)

Also,

16th term of the AP = a + (16-1)d

➡ 16th term = a + 15d

➡ a + 15d = 77 ....... (ii)

Now, subtracting equation (i) from (ii), we get,

➡ a + 15d - (a + 2d) = 77 - 12

➡ a + 15d - a - 2d = 65

➡ 13d = 65

➡ d = 5 (Keep it in mind)

Hence, the common difference we get here is 5.

Now, substituting d in equation (i), we get,

➡ a + 2×5 = 12

➡ a + 10 = 12

➡ a = 2 (Remember)

Hence, the first term of the AP is 2.

So,

Second Term=2+5=7

Third Term = 7+5 = 12

Fourth Term = 12+5 = 17 and so on.

Hence, the AP will be,

2 7 12 17 22...