What is conclude the difference between any two consecutive terms in an AP .
Find the number of terms in an arithmetic progression.
Prove the fact that in an AP, the difference between any two consecutive terms is a constant.
Important Arithmetic Progression Solutions for Class 10th.
Find the number of terms in each of the following APs : 7, 13, 19, . . . , 205
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Here, a = 7 and d = 13 – 7 = 6.
Let, the total number of terms in the A.P. is n.
Therefore, a_n = 205
⇒ a + (n – 1)d = 205
⇒ 7 + (n – 1)(6) = 205
⇒ (n – 1)(6) = 198
⇒ n – 1 = 33 ⇒ n = 34
Hence, there are 34 terms in the given A.P.