In an AP the sum of first n terms is 3 n- 2 - 2-5 n - 2

Let the sum of n terms be given by Sn so Sn = 3n²/2+ 5n/2 S1 = 3(1)²/2 + 5(1)/2 = 3/2+5/2 = gt; 4 so 1st term is 4 say 'a' Now S2 = 3(2)²/2 + 5(2)/2 = 6 ...

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Standard X

Mathematics

General Form of an AP

In an AP the ...

Question

In an AP the sum of first n terms is $3 n^{2} \div 2 + 5 n \div 2$ then find the $25^{t h}$ term.

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Solution

Let the sum of $n$ terms be given by $S_{n}$
so
$S_{n} = 3 n ² / 2 + 5 n / 2$
$S_{1} = 3 (1) ² / 2 + 5 (1) / 2$
$= 3 / 2 + 5 / 2 = 4$
So 1st term is 4 say $^{'} a^{'}$
Now
$S_{2} = 3 (2) ² / 2 + 5 (2) / 2$
$= 6 + 5 = 11$

Now $a_{2} = S_{2} - a_{1}$
$=> a_{2} = 11 - 4 = 7$

Now common difference (d)
$= a_{2} - a_{1} = 7 - 4 = 3$

we know , $n$ th term of A.P. is given as,
$a_{n} = a + (n - 1) d$
So ,
$a_{25} = 4 + (25 - 1) (3)$
$\Rightarrow a_{25} = 4 + 24 \times 3 = 4 + 72$
Hence, 25th term of the AP is $76$

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In an AP the sum of first n terms is 3n2÷2+5n÷2 then find the 25th term.

In an AP the sum of first n terms is $3 n^{2} \div 2 + 5 n \div 2$ then find the $25^{t h}$ term.