If {9^{th}} term of an A.P. is 35 and {19^{th}} is 75 , then its {20^{th}} terms will be

English

Gujarati

Hindi

8. Sequences and Series

easy

If the ${9^{th}}$ term of an $A.P.$ is $35$ and ${19^{th}}$ is $75$, then its ${20^{th}}$ terms will be

A

$78$

B

$79$

C

$80$

D

$81$

Solution

(b) ${T_9} = a + 8d = 35$ and ${T_{19}} = a + 18d = 75$

Solving the equations, we get $d = 4$ and $a = 3$

Hence ${20^{th}}$ term of $A.P.$ ,

$a + 19d = 3 + 19 \times 4 = 79$.

Standard 11

Mathematics

Share

Similar Questions

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day, $4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

medium

If $a_1, a_2, a_3 …………$ an are in $A.P$ and $a_1 + a_4 + a_7 + …………… + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

medium

(JEE MAIN-2019)

If the first, second and last terms of an $A.P.$ be $a,\;b,\;2a$ respectively, then its sum will be

easy

If ${\log _3}2,\;{\log _3}({2^x} – 5)$ and ${\log _3}\left( {{2^x} – \frac{7}{2}} \right)$ are in $A.P.$, then $x$ is equal to

medium

(IIT-1990)

If $n$ be odd or even, then the sum of $n$ terms of the series $1 – 2 + $ $3 – $$4 + 5 – 6 + ……$ will be

easy