Question

write an arithmetic sequence whose sum of first 6 terms is 300 and the first term is 30

Answer 1

Step-by-step explanation:

a = 30

S₆ = 300

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

$S₆ = \frac{6}{2} [2(30) + (6 - 1)d]$

$300 = 3[60 + 5d]$

$300 = 180 + 15d$

$120 = 5d$

$\frac{120}{5} = d$

$24 = d$

hence

$d = 24$

T₁=30

T₁=a=30

T₁=30

T₂=30+(2-1)24=30+24 = 54

T₃=30+(3-1)24=30+48 = 78

T₄=30+(4-1)24=30+72 = 102

T₅=30+(5-1)24=30+96 = 126

T₆=30+(6-1)24=30+120= 150

as Tn=a+(n-1)d

series will be

: 30,54,78,102,126,150,...

where a=first term=30 and d=difference=24