Class 10

Math

All topics

Arithmetic Progressions

Sr. no. | $a$ | $d$ | $n$ | $a_{n}$ |

(i) | 7 | 3 | 8 | ---- |

(ii) | -18 | ---- | 10 | 0 |

(iii) | ---- | -3 | 18 | -5 |

(iv) | -18.9 | 2.5 | ---- | 3.6 |

(v) | 3.5 | 0 | 105 | ---- |

(i) $a=7,d=3,n=8,a_{n}=?$

We know that,

For an A.P. $a_{n}=a+(n−1)d$

$=7+(8−1)3$

$=7+(7)3$

$=7+21=28$

Hence, $a_{n}=28$

(ii) Given that

$a=−18,n=10,a_{n}=0,d=?$

We know that,

$a_{n}=a+(n−1)d$

$0=−18+(10−1)d$

$18=9d$

$d=918 =2$

Hence, common difference, $d=2$

(iii) Given that

$d=−3,n=18,an=−5$

We know that,

$a_{n}=a+(n−1)d$

$−5=a+(18−1)(−3)$

$−5=a+(17)(−3)$

$−5=a−51$

$a=51−5=46$

Hence, $a=46$

(iv) $a=−18.9,d=2.5,a_{n}=3.6,n=?$

We know that,

$a_{n}=a+(n−1)d$

$3.6=−18.9+(n−1)2.5$

$3.6+18.9=(n−1)2.5$

$22.5=(n−1)2.5$

$(n−1)=2.522.5 =9$

$n−1=9$

$n=10$

Hence, $n=10$

(v) $a=3.5,d=0,n=105,a_{n}=?$

We know that,

$a_{n}=a+(n−1)d$

$a_{n}=3.5+(105−1)0$

$a_{n}=3.5+104×0$

$a_{n}=3.5$