Question

If sum of n terms of Ap is given by 3n2+5n then find the common diffrence and the 25th term

Answer 1

sn=3n^2+5n
s1=a1=3(1)^2+5(1)=8
s2=3(2)^2+5(2)=22
s2=22=a1+a2
a2=228=14
d=a2-a1=14-8=6
25th term =a+(n-1)d
25th term =8+(25-1)6
25th term =8+144
25th term =152

Answer 2

Solution:

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Given:

sum of n terms of an AP is given by 3n²+5n,

=> $S_n = 3n^2 + 5n$,

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To find :

The common difference(d) and 25th term ($a_{25}$)

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If we substitute,

n = 1,

we get $S_1 = a_1$,

=> $S_1 = a_1 = 3(1)^2 + 5(1)$

=> $3 + 5$

=> $8$

∴ $a = 8$

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=> $S_2 = 3(2)^2 + 5(2)$

=> $3(4) + 10$

=> $12 + 10$

=> $22$

$S_2 = a_1 + a_2$

=> $22 = 8 + 8 + d$

=> $22 = 16 + d$

=> ∴ $d = 6$

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$a_{25} = a + (25 - 1)d$

=> $a_{25} = 8 + (24)(6)$

=> $a_{25} = 8 + 144$

=> $a_{25} = 152$ ...

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