Arithmetic Progressions
Question 1:
Fill in the blanks in the following table, given that a is the first term, d the common difference and a_{n} the n^{th} term of the A.P.
a 
d 
n 
a_{n} 

I 
7 
3 
8 
…... 
II 
− 18 
….. 
10 
0 
III 
….. 
− 3 
18 
− 5 
IV 
− 18.9 
2.5 
….. 
3.6 
V 
3.5 
0 
105 
….. 
Answer:
I. a = 7, d = 3, n = 8, a_{n} = ?
We know that,
For an A.P. a_{n} = a + (n − 1) d
= 7 + (8 − 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, a_{n} = 28
II. Given that
a = −18, n = 10, a_{n} = 0, d = ?
We know that,
a_{n} = a + (n − 1) d
0 = − 18 + (10 − 1) d
18 = 9d
Hence, common ...
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