Question

if an=2n-1, then the value of sio is
A) 55
B) 95
C) 100
D) 110
24.The sum of the first n terms of​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{If \: a_n = 2n - 1 \: then \: the \: value \: of \: S_{10} \: is}$

A) 55

B) 95

C) 100

D) 110

EVALUATION

Here it is given that

$\sf{a_n = 2n - 1 }$

Putting n = 1 , 2 , 3 ... we get

First term = 2 - 1 = 1

Second Term = 4 - 1 = 3

Third term = 6 - 1 = 5

So on..

So this is an arithmetic progression

First term = a = 1

Common Difference = d = 3 - 1 = 2

Thus we get

Sum of first 10 terms

$\sf{ = S_{10}}$

$\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }$

$\displaystyle \sf{ = \frac{10}{2} \bigg[ (2 \times 1) + (10 - 1) \times 2\bigg] }$

$\displaystyle \sf{ = 5 \times (2 + 18)}$

$\displaystyle \sf{ = 5 \times 20}$

$= 100$

FINAL ANSWER

Hence the correct option is C) 100

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