Question

If the tenth and 11th term of an ap are 23 and 27 write the sum of first 20 terms​

Answer 1

a10=23

a11=27

a10=a+9d

a11=a+10d

a+10d-a-9d=27-23

d=4

substitute the value of d-

a+9d=23

a+36=23

a=-13

now finding sum-

Sn=n/2{2a+(n-1)d}

S20=10{-26+19*4)

=10{76-26}

=10{50}

=500

Answer 2

Answer:

Given:a10=23

a+9d=23. (1)

a11=27

a+10d=27. (2)

BY SOLVING WE GET:

d=4

SUBSTITUTE d=4 in (1)

a+9×4=23

a=23-36

a=-13

NOW SUM OF 20 TERMS

S20=20/2(2×-13+19×4)

S20=10(-26+76)

S20=10(50)

S20=500.