24. In an AP the first element is 5. There are 15 terms. The sum is 390. Find the common difference and the value of the middle term.
Correct Answer: Description for Correct answer:
Here a=5, n=15, \( \Large S_{n} \) = 390
\( \Large S_{n} =\frac{n}{2} \left(2a \left(n-1\right)d \right) \)
\( \Large 390 = \frac{15}{2}\{ 10+ \left(15-1\right)d \} \)
\( \Large 780 = 15 \left(10+14d\right) \)
\( \Large 10+14d = 52 \)
14d = 52-10 = 42
\( \Large d = \frac{42}{14}=3 \)
To find the middle term (i.e.) \( \Large t_{8} \)
\( \Large t_{8} = a+ \left(n-1\right)d \)
\( \Large 5+ \left(8-1\right)3 \)
= 5 + 21 = 26
Therefore, The common difference is 3 and the middle term is 26.
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