The 3rd and 9th term of an arithmetic progression are -8 and 10 respectively. What is the 16th term?
A. 34
B. 28
C. 25
D. 31
Answer: Option D
Solution(By Examveda Team)
Let the first term of an AP = a and the common difference = d3th term of AP = A3 = a + 2d = -8 ......(1)
9th term = A9 = a + 8d = 10 ...... (2)
Subtracting equation (1) from (2), we get :
⇒ 8d - 2d = 10 - (-8)
⇒ 6d =18
⇒ d = $$\frac{{18}}{6}$$ = 3
Substituting it in equation (2),
⇒ a = 10 - 8(3)
= 10 - 24
= -14
∴ 16th term = A16 = a + 15d
= -14 + 15(3)
= -14 + 45
= 31
Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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