For a given A.P.,the 11^{th} term is 38 and t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For the given $A.P.$,the $11^{th}$ term $T_{11} = 38$ and the $16^{th}$ term $T_{16} = 73$.For an $A.P.$,the common difference $d$ is given by:$d

Vedclass · Accepted Answer

$178$

Vedclass · Answer

(D) For the given $A.P.$,the $11^{th}$ term $T_{11} = 38$ and the $16^{th}$ term $T_{16} = 73$.For an $A.P.$,the common difference $d$ is given by:$d = \frac{T_{m} - T_{n}}{m - n}$Substituting $m = 16$ and $n = 11$:$d = \frac{T_{16} - T_{11}}{16 - 11} = \frac{73 - 38}{5} = \frac{35}{5} = 7$Now,using the formula for the $n^{th}$ term $T_{n} = a + (n - 1)d$:$T_{11} = a + 10d$$38 = a + 10(7)$$38 = a + 70$$a = 38 - 70 = -32$Finally,find the $31^{st}$ term $T_{31}$:$T_{31} = a + 30d$$T_{31} = -32 + 30(7)$$T_{31} = -32 + 210 = 178$Thus,the $31^{st}$ term of the $A.P.$ is $178$.

For a given $A.P.$,the $11^{th}$ term is $38$ and the $16^{th}$ term is $73$. Find the $31^{st}$ term of the $A.P.$

Similar Questions

In a flower bed,there are $23$ rose plants in the first row,$21$ in the second,$19$ in the third,and so on. There are $5$ rose plants in the last row. How many rows are there in the flower bed?

Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

For any $A.P.$,$T_{25} - T_{20} = \ldots \ldots \ldots$

For the $AP: -3, -7, -11, \ldots,$ can we find $a_{30} - a_{20}$ directly without actually finding $a_{30}$ and $a_{20}$? Give reasons for your answer.

The $15^{th}$ term of the $A.P.$ $1, 11, 21, 31, \dots$ is........

Vedclass Test Series

Exam Paper Generator

Online Exam Module