The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the 41th term of that A.P. Solve the word problem
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11th term of AP = a + (n - 1)d
16 = a + (11 - 1)d
16 = a + 10d. -(1)
21st term of AP = a + (n - 1)d
29 = a + (21 - 1)d
29 = a + 20d. -(2)
Solving both equations
a + 10d = 16
a + 20d = 29
(-) (-) (-)
-------------------
-10d = -13
d = 1.3
Putting the value of d in 1st equation.
a + 10d = 16
a + (10*1.3) = 16
a + 13 = 16
a = 3
41st term of AP = a + (n-1)d
= 3 + 40*1.3
= 55
16 = a + (11 - 1)d
16 = a + 10d. -(1)
21st term of AP = a + (n - 1)d
29 = a + (21 - 1)d
29 = a + 20d. -(2)
Solving both equations
a + 10d = 16
a + 20d = 29
(-) (-) (-)
-------------------
-10d = -13
d = 1.3
Putting the value of d in 1st equation.
a + 10d = 16
a + (10*1.3) = 16
a + 13 = 16
a = 3
41st term of AP = a + (n-1)d
= 3 + 40*1.3
= 55
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