1) If the nth and 13th terms of an AP are 34 and 64
respectively. then its 18th term is .......
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Answer:
18th term is 89.
Step-by-step explanation:
It is given that 7th & 13th terms are 34 & 64.
t7 = 34
t13 = 64
tn = a + (n - 1) * d
=> 34 = a + (7 - 1) * d
=> 34 = a + 6d .... (1)
Now
t13 = a + (13 - 1) * d
=> 64 = a + 12 * d
=> 64 = a + 12d ......(2)
Subtract eqn (1) from eqn (2)
a + 12d = 64
a + 6d = 34
=> 0 + 6d = 30
=> 6d = 30
=> d = 30/6
=> d = 5
Put d = 5 in (1)
a + 6d = 34
=> a + 6 * 5 = 34
=> a + 30 = 34
=> a = 34 - 30
=> a = 4
Now,
tn = a + (n - 1) * d
=> t18 = 4 + (18 - 1) * 5
=> t18 = 4 + 17 * 5
=> t18 = 4 + 85
=> t18 = 89
Hence,
18th term is 89.
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