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The 9th term exceeds the fifth term of an AP by 32. The sum of the ninth and fifth terms is 114. Find the eight term of the AP. ?
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- 60
- 63
- 65
- 68
Correct Option: C
T9 = a + (9 - 1)d = a + 8d
T5 = a + (5 - 1)d = a + 4d
T9 - T5 = 32
⇒ (a + 8d) - (a + 4d) = 32
⇒ 4d = 32
∴ d = 8
T9 + T5 = (a + 8d) + (a + 4d)
= 2a + 12d
T9 + T5 = 114
⇒ 114 = 2(a + 6d)
⇒ a + 6d = 57
∴ T8 = a + 7d
= a + 6d + d
= 57 + 8 = 65
