Question

in an ap the sum of n terms is 5n2/2+3n/2 find the 17 th term
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Answer 1

Step-by-step explanation:

Sum of 1 term = 5*1/2 + 3(1)/2 = 8/2 = 4 . Sum of two terms = 5(4)/2 + 3(2)/2 = 10+3 = 13 . Second term = 13 - 4 = 9 . ... 20 th term = a + ( 20 - 1 )d = a+19d = 4 + 19(5) = 99 .

Answer 2

Solution

Let the series of an arithmetic progression from the first to the last term be $S_{n}$.

Then,

• $a_{n}=S_{n}-S_{n-1}$ where $n\geq 2$.

Given: $S_{n}=\dfrac{5}{2} n^2+\dfrac{3}{2} n$

$\implies S_{n-1}=\dfrac{5}{2} (n-1)^2+\dfrac{3}{2} (n-1)$

$\implies S_{n-1}=\dfrac{5}{2} n^2-5n+\dfrac{5}{2} +\dfrac{3}{2} n-\dfrac{3}{2}$

$\implies S_{n-1}=\dfrac{5}{2} n^2-\dfrac{7}{2} n+1$

Now we have,

• $S_{n}=\dfrac{5}{2} n^2+\dfrac{3}{2} n$
• $S_{n-1}=\dfrac{5}{2} n^2-\dfrac{7}{2} n+1$

Thus,

$a_{n}=S_{n}-S_{n-1}$

$\implies \boxed{a_{n}=5n-1}$

The 17th term of the arithmetic progression is $\boxed{a_{17}=84}$.