Question

The sum of 5th and 9th terms of an ap is 30 if its 25th term is three times its 8th term find the AP.​

Answer 1

Answer:

If two powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents.

Answer 2

Question:-

The sum of 5th and 9th terms of an ap is 30 if its 25th term is three times its 8th term find the AP.

Given:-

The sum of 5th and 9th terms of an AP is 30.

25th term is three times its 8th term.

To Find:-

The AP

Solution:-

Adding (i) and (ii):-

$\sf \implies 2a + 12d - 2a + 3d = 30$

$\sf \implies 15d = 30$

$\sf \implies d = \dfrac{30}{15}$

$\sf \implies d = 2$

Substitute d = 2 in equation (i)

$\sf \implies 2a + 12d = 30$

$\sf \implies 2a + 12(2) = 30$

$\sf \implies 2a = 30 - 24$

$\sf \implies 2a = 6$

$\sf \implies a = \dfrac{6}{2}$

$\sf \implies a = 3$

• The first term = a = 3

• The second term = a + d = 3 + 2 = 5

• The third term = a + 2d = 3 + 4 = 7