Question

Find the sum of the first 24 terms of the AP: 8,3,-2….

Answer 1

$\huge{\underline{\bf\red{QuestiØn} :}}$

$\sf Find \: the \: sum \: of \: first \: 24 \: terms \\ \sf of \: the \: AP : 8,3, - 2, .......$

$\huge{\underline{\bf\blue{SolutiØn}\ :}}$

We have,

• first term, $\sf a_{1} = 8$

• second term, $\sf a_{2} = 3$

• common difference, $\begin{aligned} \sf d & = a_{2} - a_{1} \\ & =3 - 8 \\ &= - 5 \\ \end{aligned}$

• no. of terms, $\sf n = 24$

Hence ,

Sum of first 24 terms,

$\begin{aligned} \\ \quad \sf S_{24}& = \sf \frac{n}{2} \bigg[a_{1} + (n - 1)d \bigg] \\ \\ & = \frac{24}{2} \bigg[8 + (24 - 1)( - 5) \bigg] \\ \\ & = \frac{ {}^{12} \ \cancel{24}}{_{1} \ \cancel{2}} \bigg[8 + (24 - 1)( - 5) \bigg] \\ \\ & = 12[8 + 23( - 5)] \\ \\ & = 12[8 - 115] \\ \\ & = 12( - 107) \\ \\ & = \boxed{ \bf{ - 1284}} & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

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