Question

The 5th term of an Ap. is 22 and 9th Term is 14. find 16th term of an A.P​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

16th term of the A. P. is 0

Explanation:

Given,

5th term of an A. P. = 22

9th term of an A. P. = 14

We know,

nth term of an A. P. :-

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

Where,

• n denotes the nth term
• a is the first term
• d is the common difference.

Then, for the first case :-

$\sf \implies \: 22 = a + (5 - 1)d$

$\sf \implies \: 22 = a + (4)d$

$\sf \implies \: 22 = a + 4d \bf . . . .(i)$

And also, for the second case :-

$\sf \implies \: 14 = a + (9 - 1)d$

$\sf \implies \: 14 = a + (8)d$

$\sf \implies \: 14 = a + 8d \bf . . . . (ii)$

On subtracting eq.(i) by (ii) :-

$\sf \: a + 4d = 22 \\ \sf \underline{\: a + 8d = 14} \\ \sf\implies - 4d = 8 \\ \sf \implies \: d = \frac{8}{ - 4} \\ \sf \therefore \: d = - 2$

Substituting ‘d’ in eq.(i) :-

$\sf \implies \: a + 4d = 22$

$\sf \implies \: a + 4( - 2) = 22$

$\sf \implies \: a - 8= 22$

$\sf \implies \: a = 22 + 8$

$\sf \implies \: a = 30$

Therefore,

16th term of the A. P. is :-

$\sf \longrightarrow \: a + (n - 1)d$

$\sf \longrightarrow \: 30 + (16 - 1)( - 2)$

$\sf \longrightarrow \: 30 + (15)( - 2)$

$\sf \longrightarrow \: 30 - 30$

$\sf \longrightarrow \: 0$

∴ 16th term of the A. P. is 0