In a progression ,if an=2n2+1,then S2 is -----------
Answers
Answer:Sol:
Sum of n terms = 2n2 + 2
S1 = Sum of the series with one term = 2(1)2 + 2 = 4
S2 = Sum of the series with two terms = 2(2)2 + 2 = 10
S3 = Sum of the series with three terms = 2(3)2 + 2 = 20
T1 = S2 - S1 = 10 - 4 = 6
T2 = S3 - S2 = 20 - 10 = 10
Common difference = t2 - t1 = 10 - 6 = 4
A.P. = 6, (6 + 4), (6 + 8), (6 + 12)......
Hence, the required arithmetic progression is 6, 10, 14, 18, .........
Step-by-step explanation:
Answer:
therefore answer 12
Step-by-step explanation:
Correct option is
B
12
Given a
n
=2n
2
+1 (1)
Put n=1 in (1), we get,
a
1
=2(1)
2
+1
∴a
1
=2+1
∴a
1
=3
Put n=2 in (1), we get,
a
2
=2(2)
2
+1
a
2
=2(4)+1
∴a
2
=9
Thus, d=a
2
−a
1
∴d=9−3
∴d=6Now, sum of n terms of A.P. is,
S
n
=
2
n
[2a+(n−1)d]
Put n=2 in above equation, we get,
S
2
=
2
2
[2a+(2−1)d]
∴S
2
=1[(2×3)+(1×6)]
∴S
2
=1[6+6]
∴S
2
=12