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How many terms are there in the AP, $7, 13, 19, . . ., 205$ ?

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32

33

34

35

answer is C.

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Detailed Solution

The given sequence is,

7, 13, 19, . . ., 205

.
Here, the first term,

a = 7

and the common difference,

d = 6

.
The last term,

=

205

.
Let

n^{th}

term be the last term of the given AP.
We know that the

n^{th}

term of an AP is given by,

a + (n - 1) d

⇒

a + (n - 1) d = 205

⇒

7 + (n - 1) \times (6) = 205

⇒

7 - 6 + 6 n = 205

⇒

1 + 6 n = 205

⇒

6 n = 205 - 1

⇒

n = \frac{204}{6}

⇒

n = 34

⸫ The number of terms in the given sequence is

34

.
Hence, the correct option is 1.

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