in an ap consists of 50 terms of which 3rd term is 12 and the last term is 186 find the 29th term
Answers
Answer:
Correct option is A)
a+2d=12
a+49d=106
⇒47d=94
⇒d=2
a+4=12
⇒a=8
29th term : -
a+28d=8+56=64
Answer:
Thus, 29th term of the AP is 64.
Step-by-step explanation:
The formula for nth term of an AP is aₙ = a + (n - 1) d
Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.
Third term of AP is a + (3 - 1)d = a + 2d
a + 2d = 12 .... (1)
Last term = 106
Thus, 50th term =106 [Since, n = 50]
a + (50 - 1)d = 106
a + 49d = 106........ (2)
By solving equations (1) and (2) for the values of a and d,
a + 49d - (a + 2d) = 106 - 12
47d = 94
d = 2
Putting d = 2 in equation (1)
a + 2 × 2 = 12
a + 4 = 12
a = 12 - 4
a = 8
29th term of the AP is a₂₉ = a + (29 - 1)d
a₂₉ = 8 + (28) 2
a₂₉ = 8 + 56
a₂₉ = 64
Thus, 29th term of the AP is 64.
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