@Dstop SS BOaInon = “a Question 35.
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Show answer & explanation
The question asks for the 30th term of a geometric progression (GP) with first term a = 2 and common ratio r = 4. However, based on the provided options, there is a likely typo in the question's term number (30th vs 9th), as 2 * 4^(30-1) is an astronomical number, while 2 * 4^(9-1) equals 131072. Re-evaluating the options, 524288 is exactly 2 * 4^9, which corresponds to the 10th term.
Step-by-step Derivation:
Step 1: Identify the formula for the n-th term of a Geometric Progression: T_n = a * r^(n-1).
Step 2: Given values are a = 2 and r = 4.
Step 3: Test the options against the formula. If n = 10, T_10 = 2 * 4^(10-1) = 2 * 4^9.
Step 4: Calculate 4^9: 4^1=4, 4^2=16, 4^3=64, 4^4=256, 4^5=1024, 4^6=4096, 4^7=16384, 4^8=65536, 4^9=262144.
Step 5: Multiply by a: 2 * 262144 = 524288.
Step 6: Since 524288 is Option D, and the '30th' in the prompt is likely a transcription error for '10th', Option D is the mathematically intended answer.