Question

First term of the arithmetic sequence is 40 and sum of first 6 terms is 290. a) find 3rd term? b)write first five terms of the sequence?

Answer 1

Step-by-step explanation:

let common difference = d

1st term = t1 = a = 40

sum of first 6 terms = S6 = 290

=> S6 = 6(2×40+5d)/2 = 290

=> 3(80+5d) = 290

=> 80+5d = 290/3

=> 5d = 290/3 - 80 = 50/3

=>d = 50/(5×3) = 10/3

a) 3rd term = t3 = a+2d = 40+2×10/3 = 40+20/3 = 140/3

b) first five terms of the sequence

t1 = 40 = 120/3

t2 = 40+d = 40 + 10/3 = 130/3

t3 = 40+2d = 40+2×10/3 = 40+20/3 = 140/3

t4 = 40+3d = 40+3×10/3 = 40+10 = 50 = 150/3

t5 = 40+4d = 40+4×10/3 = 40+40/3 = 160/3