Sequences and Series — Important Questions

Common difference is constant, Each term is obtained by adding d to previous term, Sum of equidistant terms from ends is constant, nth term is linear in n

In AP: difference between consecutive terms is constant, terms are formed by adding d, equidistant terms sum to same value, nth term an = a + (n-1)d is linear. Terms increase arithmetically, not exponentially.

13th term

Step 1: a = 5, d = 3, an = 41. Step 2: Use 41 = 5 + (n-1)×3. Step 3: 36 = (n-1)×3, so n-1 = 12, therefore n = 13.