Question

If 8 times the eighth term of an



a.P is equal to 15 time its fifteenth term. Find uts 23rd term.

Answer 1

Hey, there!

Here's your answer.

Let the 1st term be a and common difference be d.

So, 8th term = a + 7d

and 15th term is = a + 14d

☛ According to the question,

8 × (a + 7d) = 15 × (a + 14d)

8a + 8×7d = 15a + 15×14d

15a - 8a = 8×7d - 15×14d = 14(4d - 15d)

7a = 14(-11d)

a = -22d

☛ So, 23rd term will be

= a + 22d

= -22d + 22d = 0 (ans)

Hope that helps.

Thanks.

Answer 2

Let a be the first term and d be their common difference of the AP.

Then, nth term of the AP TT =a+(n−1)d

Given, 8×T8 =12×T 12

=>8(a+(8−1)d)=12(a+(12−1)d)

=>8(a+7d)=12(a+11d)

=>2(a+7d)=3(a+11d)

=>2a+14d=3a+33d

=>a=−19d

So, T 20 =a+(20−1)d=−19d+19d=0