Add 7+10*1/2+14+....+84.
Answers
Here, a=7 ,d=7/2 , an=84 , Sn=?
We know that,
an = a+(n-1)d
84 = 7+(7/2n) -7/2
77+7/2 = 7/2n
154-7/2 =7/2n
n = 21
Sn= n/2 [a+an]
Sn= (21/2) * 91
Sn= 1911 / 2
So, the sum of 7+21/2+14+.............+84 is 1911/2
Answer:
GIVEN:−
\large\tt\purple{a=7}a=7
\large\tt\purple{d=10\frac{1}{2}-7=\frac{21}{2}-7=\frac{7}{2}}d=10
2
1
−7=
2
21
−7=
2
7
\small\sf\underline\pink{Let\:the\:nth\:term\:of\:the\:AP\:is\:84}
LetthenthtermoftheAPis84
\therefore∴ \large\tt\orange{an=84}an=84
\longrightarrow⟶ \large\tt\orange{a+(n-1)d=84}a+(n−1)d=84
\longrightarrow⟶ \large\tt\orange{7+(n-1)( \frac{7}{2} )=84}7+(n−1)(
2
7
)=84
\longrightarrow⟶ \large\tt\orange{(n-1)(\frac{7}{2)}=77}(n−1)(
2)
7
=77
\longrightarrow⟶ \large\tt\orange{n-1=22}n−1=22
\longrightarrow⟶ \large\tt\orange{n=23}n=23
\small\sf\underline\pink{The\:sum\:of\:n\:terms\:of\:an\:AP\:is\:given\:by}
ThesumofntermsofanAPisgivenby
\longrightarrow⟶ \large\tt\gray{Sn=\frac{n}{2}(a+l)}Sn=
2
n
(a+l)
\longrightarrow⟶ \large\tt\gray{\frac{23}{2}(7+84)}
2
23
(7+84)
\longrightarrow⟶ \large\tt\gray{S23=\frac{23}{2}(91)}S23=
2
23
(91)
\longrightarrow⟶ \large\tt\gray{S23=\frac{2093}{2}=1046\frac{1}{2}}S23=
2
2093
=1046
2
1