Question

the second and third terms of arthematic progression are 14 and 18 respectively . find the sum of first 51 terms of this arthematic progression​

Answer 1

Given:-

• a+d=14 -(1)
• a+2d=18-(2)

To find:-

• sum of 51 term of AP

solution:-

solve eq (1) and (2)

common difference?

a+2d=18

a+d=14

- - -

d=4

hence the common difference is 4

now value of a?

in eq (1)

a+d=14

a+4=14

a=10

hence first term of AP is 10

now sum of 51 term ?

formula

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

S(n)=$\frac{51}{2}$ [2×10+(51-1)4]

S(n)=$\frac{51}{2}$ [20+(50)4]

S(n)=$\frac{51}{2}$ [20+200]

S(n)=$\frac{51}{2}$ [220]

S(n)=51 ×[110]

S(n)=5610

Thanks

$hope\: its\: helpful$

Answer 2

sum of 51 terms is 5610

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