A 8th term of an A.P is 380 and the 12th term is 58 ,find the 30th term

Answer 1

To find the 30th term of an arithmetic progression (A.P.), we need to find the common difference (d) first.

Given that the 8th term is 380 and the 12th term is 58, we can form two equations:

Eighth term: a + 7d = 380 (since the 8th term is a + 7d)
Twelfth term: a + 11d = 58 (since the 12th term is a + 11d)

To solve these two equations, we can subtract the second equation from the first equation:

(a + 7d) - (a + 11d) = 380 - 58
a + 7d - a - 11d = 322
-4d = 322
d = -322/4
d = -80.5

Now that we have the common difference, we can find the first term (a). We can substitute the value of d into one of the equations:

a + 11d = 58
a + 11(-80.5) = 58
a - 885.5 = 58
a = 58 + 885.5
a = 943.5

So, the first term (a) is 943.5 and the common difference (d) is -80.5.

Now, we can find the 30th term by using the formula for the nth term of an A.P:

nth term = a + (n - 1)d

Substituting the values:

30th term = 943.5 + (30 - 1) * -80.5
= 943.5 + 29 * -80.5
= 943.5 - 2334.5
= -1391

Therefore, the 30th term of the A.P. is -1391.