Find the sum of frist 51 terms of the AP whose 2nd term is 2 and 4th term is 8
Answers
Answer:
3774
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Step-by-step explanation:
a = 1st term d = difference
an = a + (n-1)d
a+d = 2 ,
a+3d=8
2d=6
d = 3
a=-1
51 term =-1+50*3=149
Sum = (n/2)(ist term + Last Term)
Sum = (51/2)(-1+149)
=51*148/2
= 51*74
= 3774
Answer:
Step-by-step explanation:
let's consider first term= t1= 'a' and common difference be 'd'
total number of terms we've to find out = 51
therefore , n = 51
as per first condition,
t2 = 2
a + (2-1)d= 2 ___________ formula
a + d = 2_______1
as per second condition,
a + (4-1)d = 8______formula
a + 3d = 8_______2
subtracting eqn. 1 from 2,
a + 3d = 8
- a + d = 2
2d = 6
d = 3
substituting d=3 in eqn. 1
a + d = 2
a + 3 = 2
a = 2 - 3
a = -1
Sn = n/2 [ 2a + (n - 1) d ] _________ formula
S51 = 51/2 [ 2 x (-1) + (51 - 1) x 3]
=51/2 [ -2 + 50 x 3 ]
= 51/2 [ -2 + 150 ]
= 51/2 x 148
= 51 x 74 ___________ dividing 148 by 2
= 3774
S51 = 3774