Question

7+10 1/2 + 14 +....+84​

Answer 1

$\large\sf\underline\red{GIVEN:-}$

$\large\tt\purple{a=7}$

$\large\tt\purple{d=10\frac{1}{2}-7=\frac{21}{2}-7=\frac{7}{2}}$

$\small\sf\underline\pink{Let\:the\:nth\:term\:of\:the\:AP\:is\:84}$

$\therefore$$\large\tt\orange{an=84}$

$\longrightarrow$$\large\tt\orange{a+(n-1)d=84}$

$\longrightarrow$$\large\tt\orange{7+(n-1)( \frac{7}{2} )=84}$

$\longrightarrow$$\large\tt\orange{(n-1)(\frac{7}{2)}=77}$

$\longrightarrow$$\large\tt\orange{n-1=22}$

$\longrightarrow$$\large\tt\orange{n=23}$

$\small\sf\underline\pink{The\:sum\:of\:n\:terms\:of\:an\:AP\:is\:given\:by}$

$\longrightarrow$$\large\tt\gray{Sn=\frac{n}{2}(a+l)}$

$\longrightarrow$$\large\tt\gray{\frac{23}{2}(7+84)}$

$\longrightarrow$$\large\tt\gray{S23=\frac{23}{2}(91)}$

$\longrightarrow$$\large\tt\gray{S23=\frac{2093}{2}=1046\frac{1}{2}}$