Question

given a = 7, a13 =35, find d and S13​

Answer 1

Answer:

n=13

a=7

a13=35

so, a13=a+(n-1)d

or,35=7+(13-1)d

or, 12d=28

or, d=7/3

so, s13 =n/2{2a+(n-1)d}

= 13/2{14+12×7/3}

=13/2{14+28}

=13/2×42

=273

I hope it helps you

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Answer 2

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

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

$\large\tt\purple{a13=35}$

$\small\tt\green{The\:13th\:term\:of\:the\:AP\:is\:35}$

$\therefore$$\large\tt\orange{a13=35}$

$\longrightarrow$$\small\tt\red{a+(13-1)d=35}$

$\longrightarrow$$\small\tt\red{7+12d=35}$

$\longrightarrow$$\small\tt\red{12d=28}$

$\longrightarrow$$\small\tt\red{d=\frac{28}{12}=\frac{7}{3}}$

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

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

$\longrightarrow$$\large\sf\pink{S13=\frac{13}{2}(7+35)}$

$\longrightarrow$$\large\sf\pink{S13=\frac{13}{2}(42)}$

$\longrightarrow$$\large\sf\pink{S13=273}$