Question

Can someone help me please

Answer 1

`\sf\\\textsf{We have the following arithmetic sequence:}\\1,7,13,19,25\\\textsf{Now,}\\\textsf{Common difference(d) = second term - first term = 7 - 1 = 6}\\\textsf{First term(a) = 1}\\\textsf{So,}\\\textsf{nth term}(t_n)=a+(n-1)d\\\textsf{or, }t_n=1+(n-1)* 6\\\textsf{or, }t_n=1+6n-6\\\therefore\ t_n=6n-5`

`\sf\\\textsf{In the question we are given 5 terms. And we are asked to find the three terms }\\\textsf{after these 5 numbers. So, we need to find }t_6,\ t_7\textsf{ and }t_8.`

`\sf\\\therefore\ t_6=6(6)-5=31, t_7=6(7)-5=37\ and\ t_8=6(8)-5=43\\`

`\textsf{So the next three terms are 31, 37 and 43.}`