MP Board · Class 10 · Mathematics · Arithmetic ProgressionsFind the value of 'a' in the given AP: 3, 6, 9, 12, ... , 48. Also, find the number of terms in the AP.
Step-by-Step Solution
Step 1: Identify the first term and common difference of the AP.\nThe first term of the AP is 3, and the common difference is 3.
Step 2: Use the formula for the nth term of an AP to find the value of 'a'.\nThe formula for the nth term of an AP is given by: an = a + (n - 1)d, where a is the first term, n is the number of terms, and d is the common difference.
Step 3: Substitute the values of 'a', 'd', and 'an' into the formula and solve for 'n'.
48 = 3 + (n - 1)3 45 = (n - 1)3 15 = n - 1\nn = 16
Step 4: Now that we have the value of 'n', we can find the value of 'a' using the formula for the nth term of an AP.\nan = a + (n - 1)d
48 = a + (16 - 1)3 48 = a + 45\na = 3
💡 Study Guide: This question tests core syllabus concepts from Arithmetic Progressions. For formulas, key summaries, and mock exam reference guides, read the full Arithmetic Progressions Revision Notes.