Question

find the sum of the first 22 terms of the AP:9,17,25...​

Answer 1

$\huge\tt\colorbox{pink}{Answer}$

a = 9

d = a2 - a1

d = 17 - 9

d = 8

n = 22

Sn = n/2{2a + (n - 1) d}

S22 = 22/2 {2(9) + (22 -1 ) 8}

S22 = 11 {18 + 168 }

S22 = 11 (186)

S22 = 2046

Answer 2

$\huge\purple{\textbf{\textsf{Question:}}}$

$\bf Find \: the \: sum \: of \: the \: first \: 22 \\ \bf terms \: of \: the \: AP : 9, \: \: \: 17, \: \: \: 25...$

$\huge\purple{\textbf{\textsf{Answer:}}}$

$\bf Given : \\ \bf a1 = 9 \bf \: \: \: \: \: a2 = 17 \\ \bf d = a2 - a1 = 17 - 9 \\ \bf \therefore d = 8 \\ \bf n = 22 \\ \\ \bf Formula \: to \: find \: the \: sum \: of \\ \bf first \: ‛n’ \: terms \: of \: an \: AP : \\ \\ \bf S_n = \frac{n}{2} [2a + (n - 1)d] \\ \\ \bf \implies S_{22} = \frac{22}{2} [2(9) + (22 - 1)8 \: ] \\ \\ \bf \implies S_{22} = 11[18 + (21)8 \: ] \\ \bf \implies S_{22} = 11(18 + 168) \\ \bf \implies S_{22} = 11(186) \\ \bf \therefore S_{22} = \underline{ \underline{2,046}}$

$\huge\purple{\textbf{\textsf{Hope~it~helps..!!}}}$