एक ` A.P. ` में यदि `S_n =3n^(2) +5n ` और `ak =164,` तो 'k ' का मान ज्ञात कीजिए|

Explanation

` " " S_n =3_n^(2) +5n`
`rArr" " S_n-1 =3 (n-1) ^(2) +5(n-1)`
` " " =3(n^(2) -2n +1) +5(n-1) =3n^(2) -n-2`
अब, ` " " a_n =S_n -S_(n-1) `
` " " =(3n^(2) +5n )-(3n^(2) -n -2 )=6n +2`
` rArr " " a_k =6k +2`
दिया है, ` " " a_k =164`
` rArr " " 6k +2 =164`
` rArr " " 6k =162`
` rArr" " k =27`