Arithmetic sequence worksheet solution1 :
Here we are going to see solution of each questions from the arithmetic sequence worksheet.
(1) The first term of an A.P is 6 and the common difference is 5. Find the A.P and its general term
Solution :
First term = 6
Common difference = 5
a = 6
d = 5
General form of A.P is a , a + d , a + 2 d , …………….
6 , (6 + 5) , (6 + 2(5)) , …………..
6 , 11 , (6 + 10) ,……………….
Hence the required arithmetic progression is 6, 11, 16 , …………..
(2) Find the common difference and 15 th term of an A.P 125 , 120 ,115 , 110 , ……….….
Solution :
First term = 125
a = 125
Common difference = t2 – t1
= 120 – 125
= -5
General term of an A.P
(tn) = a + (n - 1) d
15th term of the A.P = 125 + (15 - 1) (-5)
= 125 + 14 (-5)
= 125 – 70
t₁₅ = 55
Hence, 15th term of A.P is 55
(3) Which term of the arithmetic sequence is 24, 23 ¼ ,22 ½, 21 ¾, ………. Is 3?
Solution :
First term = 24
a = 24
Common difference = t2 – t1
= 23 ¼ – 24
= (93/4) – 24
= (93-96)/4
d = -3/4
tn = a + (n - 1) d
Let us consider 3 as nth term
tn = 3
3 = 24 + (n-1) (-3/4)
3 – 24 = (n-1) (-3/4)
(-21 x 4)/(-3) = n -1
84/3 = n -1
28 = n – 1
28 + 1 = n
n = 29
Hence, 29th term of and A.P is 3.
(4) Find the 12th term of the A.P √2 , 3 √2 , 5 √2 , …………
Solution :
First term (a) = √2
Common difference (d) = 3 √2 - √2 = 2 √2
n = 12
General term of an A.P
tn = a + (n - 1) d
t₁₂ = √2 + (12 - 1) (2√2)
= √2 + 11 (2√2)
= √2 + 22 √2
= 23 √2
Hence, 12th of A.P is 23 √2
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