Find the number of terms of the given AP:
$7, 13, 19...., 205$

34,27

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26,35

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27,34

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35,26

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Solution

The correct option is A
34,27

Formula to find $n^{t h}$ term of arithmetic progression is

$t_{n} = a_{1} + (n - 1) d$

where,

' $a_{1}$ ' is the first term,

'd' is the common difference,

'n' is the number of terms,

' $t_{n}$ ' is the $n^{t h}$ term.

Given, $a_{1} = 7$ , $a_{2} = 13$ , $t_{n} = 205$

d = $a_{2}$ - $a_{1}$ = 13 - 7 = 6

Substituting the values in the formula $t_{n} = a + (n - 1) d$ to find $n^{t h}$ term of arithmetic progression, we get

$205 = 7 + (n - 1) 6$
$\Rightarrow 205 = 6 n + 1$

$\Rightarrow 204 = 6 n$

$\Rightarrow n = \frac{204}{6} = 34$

Therefore, there are 34 terms in the given arithmetic progression.

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Similar questions

7, 13, 19, . . . ., 205

18, 15 \frac{1}{2}, 13, . . ., - 47

A . P . 7, 13, 19, . . . ., 205

Find the number of terms in each of the following APs:

(i) $7, 13, 19...., 205$

(ii) $18, \frac{31}{2}, 13, . . . - 47$

Find the number of terms in each of the following APs respectively:

$(i) 7, 13, 19...., 205$
$(i i) 18, \frac{31}{2}, 13, . . . - 47$

7, 13, 19, . . . .205

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