Question

If the third and 9th term of an ap are 4,-8 respectively. find a, d

Answer 1

GiveN :

• Third term (a3) = 4
• Ninth term (a9) = - 8

To FinD :

• First term (a)
• Common Difference (d)

SolutioN :

Make equations and solve them to find values of a and d

⇒a3 = a + 2d

⇒4 = a + 2d.... (1)

______________________

⇒a9 = a + 8d

⇒-8 = a + 8d.....(2)

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(2) - (1)

⇒-8 - 4 = a + 8d - ( a + 2d)

⇒-12 = a + 8d - a - 2d

⇒-12 = 6d

⇒d = -12/6

⇒d = -2

∴ Common Difference is -2.

__________________________

Put value of d in (1)

⇒4 = a + 2(-2)

⇒4 = a - 4

⇒a = 4 + 4

⇒a = 8

∴ First term is 8.