Question

consider the arithmetic sequence is 7,12,17 a) what is the common difference b) what is difference between the sum of first 20 term and the sum of next 20 term ?​

Answer 1

a) D= a_2-a_1

=12-7= 5

Common difference= 5

b)

$\tt \: = \frac{ 20 }{ 2 } (2(7)+(40-1)(5)) \\ \tt \: 10\left(2\times 7+\left(40-1\right)\times 5\right) \\ \tt \: 10\left(14+\left(40-1\right)\times 5\right)\\ \tt \:10\left(14+39\times 5\right)\\ \tt \: 10\left(14+195\right)\\ \tt \: 10\times 209 \\ \tt \:2090 --------i) \\ \\ \tt \:= \frac{ 20 }{ 2 } (2(7)+(20-1)(5))\\ \tt \:10\left(2\times 7+\left(20-1\right)\times 5\right)\\ \tt \: 10\left(14+\left(20-1\right)\times 5\right) \\ \tt \:10\left(14+\left(20-1\right)\times 5\right)\\ \tt \: 10\left(14+19\times 5\right)\\ \tt \: 10\left(14+95\right)\\ \tt \: 10\times 109 \\ \tt \:1090-------ii)$

From Eq i) and ii)

2090-1090=1000

Difference between the sum of first 20 term and the sum of next 20 term= 1000

$\sf \: @WildCat7083$