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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 2 · Q29
(A) The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term.
The sum of first $\displaystyle 15$ terms of an A.P. is $\displaystyle 750$ and its first term is 15. Find its $\displaystyle 20^{\text {th }}$ term.
Rohan repays his total loan of ₹ $\displaystyle 1,18,000$ by paying every month starting with the first instalment of ₹ $\displaystyle 1{,}000$ . If he increases the instalment by ₹ $\displaystyle 100$ every month, what amount will be paid by him in the $\displaystyle 30^{\text {th }}$ instalment ? What amount of loan has he paid after $\displaystyle 30^{\text {th }}$ instalment ?
Marking-scheme solution
\[\begin{aligned}
& a=15, S_{15}=750 \\
& \frac{15}{2}[2 a+14 d]=750 \\
& 2(15)+14 d=100 \\
& \quad d=5 \\
& a_{20}=a+19 d=15+19(5)=110
\end{aligned}
\]
A.P formed is $\displaystyle 1000$, $\displaystyle 1100$, 1200...
\[\begin{aligned}
& a=1000, d=100 \\
& a_{30}=a+29 d=3900
\end{aligned}
\]
Amount paid in \(\displaystyle 30^{\text {th }}\) instalment \(\displaystyle =₹ 3,900\)
\[\begin{aligned}
& S_{30}=\frac{30}{2}[2 \times 1000+29 \times 100]=15 \times 4900=73,500 \\
& \therefore \text { Total amount paid after } 30^{\text {th }} \text { instalment }=₹ 73,500
\end{aligned}
\]
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