Question

2N9GNH aaaa find the 31st term of an A.P whose 11th term is 38 and 16th term is 73

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Answer 1

Given :-

11th term, $\sf a_{11}$ = 38

16th term, $\sf a_{16}$ = 73

To Find :-

The 31st term of the A.P.

Solution :-

Given that,

11th term, $\sf a_{11}$ = 38

16th term, $\sf a_{16}$ = 73

We know that,

$\sf a_n = a+(n-1)d$

$\sf a_{11} = a+(11-1)d$

$\sf 38 = a+10d \qquad ...(1)$

In the same way,

$\sf a_{16} = a +(16-1)d$

$\sf 73 = a+15d \qquad ...(2)$

By subtracting equation (1) from (2), we get

$\sf 35 = 5d$

$\sf d = 7$

From equation (1), we can write,

$\sf 38 = a+10 \times (7)$

$\sf 38 - 70 = a$

$\sf a = -32$

$\sf a_{31} = a +(31-1) d$

$\sf =- 32 + 30 (7)$

$\sf = - 32 + 210$

$\sf = 178$

Hence, 31st term is 178.