Question

if the n term of an AP is 3n^2+5n and it's m term is 164 find value of m
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Answer 1

Answer:

3n^2+5n

put n=1,2,3,4.....

3×1^2+5×1

sn=8

s2=22

s3=52

t1=a=8

t2=22-8

t2=14

t3=42-22

t3=20

d=14-8=6

tm=a+(m-1)d

164=8+(m-1)6

164-8=6m-6

156+6=6m

162=6m

m=27

Answer 2

Given

Sn = 3n² + 5n

n'th term = 164

To find

the value of m

Solution

$\sf \implies S_1 = a_1 = 3(1)^2 + 5(1) = 8$

$\sf \implies S_2 =3(2)^2 + 5(2) = 22$

$\sf \implies S_2 = 22 = a_1+a_2$

$\sf\implies a_2 = 22 - 8 = 14$

$\sf \implies d = a_2 - a_1 = 14-8=6$

$\sf \implies {n}^{th}\: term = 164, \ then \: value \: of \: m?$

$\sf \implies {n}^{th} \: term = a+(m-1)d$

$\sf \implies 164 = 8+(m-1)6$

$\sf \implies \dfrac{164-8}{6} =m-1$

$\sf \implies \dfrac{156}{6} =m-1$

$\sf \implies 26 =m-1$

$\sf \implies m= 26+1$

$\sf \implies m = 27$

Therefore, 27ᵗʰ term is 164.

Hope it helps