Question

The sum of 5th and the 9th term of an ap ia 30 if its 25th is three its 8th term find the ap

Answer 1

We have been given that a5+a9=30 a+4d+a+8d=30 2a+12d=30 a+6d=15-----------------(1) Now ,a25=3a8 a+24d=3×(a+7d) a+24d=3a+21d 3d=2a a=3d/2 Putting in (1) 3d/2+6d=15 3d+12d=30 15d=30 d=2    Putting value of a (1) 15+6×2 3 So ap is 3,5,7,9

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Sum of 5th term = 30

Also

Sum of 9th term of = 30

Hence

a + 4d + a + 8d = 30

2a + 12d = 30 ....... (1)

Also we have,

${\boxed{\sf\:{25\;term\;is\;3\;times\;of\;3rd\;term}}}$

25th term= 3(8th term)

a + 24d = 3(a + 7d)

a + 24d = 3a + 21d

24d - 21d = 3a - a

3d = 2a ...... (2)

Put the value of (2) in (1)

2a + 12d = 30

3d + 12d = 30

15d = 30

d = 2

2a = 3d

2a = 3 × 2

2a = 6

a = 3

Hence,

Arithmetic Progression is 3, 5 , 7, 9