Question

write three arithmetic sequence with 90 as the sum of first 5term

Answer 1

let the five no. be

(a-2d) ,(a-d), a, (a+d) ,(a+2d) now,

=>(a-2d) +(a-d)+ a+(a+d)+(a+2d)=90

=>5a=90

a=18

now,

3 sequence =(18) ,(18+d),(18+2d)

Answer 2

$\textbf{Your answer is --}$

Let, the 5 term of an AP be

$\textbf{(a-2d),(a-d),(a),(a+d),(a+2d)}$

Since, sum of 5 term is 90

So, a-2d+a-d+a+a+d+a+2d = 90

=> 5a = 90

=> a = 90/5

=> a = 18.

also,

sum of five term is-

S5 = 5/2{2a+(5-1)d}

since, sum of 5th term is 90

So,

90 = 5/2(2×18+4d)

=> (90×2)/5 = 36 + 4d

=> 36 = 36 + 4d

=> d = 0

So, first term a = 18 and b = 0

$\textbf{Hence , the three AP sequence is }$

$\textbf{18,18,18}$

$\textbf{【 Hope it helps you 】}$