1. **Stating the problem:** We are given two sequences and asked to find the missing term in each. 2. **First sequence:** 47, 119, 167, __, 359, 527 We need to find the missing term in the fourth position. 3. **Analyzing the first sequence:** Calculate the differences between consecutive terms: $$119 - 47 = 72$$ $$167 - 119 = 48$$ Let the missing term be $x$. $$x - 167 = d_3$$ $$359 - x = d_4$$ $$527 - 359 = 168$$ 4. **Looking for a pattern in differences:** The differences are 72, 48, $d_3$, $d_4$, 168. Try to see if differences follow a pattern or ratio. 5. **Check if differences are multiples of 24:** 72 = 3*24 48 = 2*24 168 = 7*24 6. **Guessing the missing differences:** The differences might be increasing or following a pattern. Try $d_3 = 4*24 = 96$ and $d_4 = 5*24 = 120$. 7. **Check if this fits:** $$x = 167 + 96 = 263$$ $$359 - 263 = 96$$ (does not match 120) Try $d_3 = 56$ (difference between 167 and x), then $d_4 = 192$ (difference between x and 359) to check if sum matches. 8. **Try average approach:** Since 359 and 527 difference is 168, and previous differences are 72 and 48, the pattern is not linear. 9. **Try another approach:** Check if the sequence is quadratic or follows a pattern. 10. **Try to check the options:** (a) 279 (b) 281 (c) 283 (d) 287 Calculate differences with these options: - For 279: 279 - 167 = 112, 359 - 279 = 80 - For 281: 281 - 167 = 114, 359 - 281 = 78 - For 283: 283 - 167 = 116, 359 - 283 = 76 - For 287: 287 - 167 = 120, 359 - 287 = 72 11. **Check if differences form a pattern:** Differences between consecutive differences: 72, 48, ?, ?, 168 Try to see if the differences of differences are consistent. 12. **Second sequence:** 79, 71, 61, 53, 43, ? Find the missing term. 13. **Analyze second sequence:** Calculate differences: $$71 - 79 = -8$$ $$61 - 71 = -10$$ $$53 - 61 = -8$$ $$43 - 53 = -10$$ 14. **Pattern in differences:** The differences alternate between -8 and -10. 15. **Find next difference:** Since last difference was -10, next should be -8. 16. **Calculate missing term:** $$43 - 8 = 35$$ 17. **Check options:** (a) 49 (b) 37 (c) 41 (d) 31 None is 35, closest is 37 or 31. 18. **Re-examine differences:** Maybe pattern is -8, -10, -8, -10, -8, so next difference is -8. 19. **Try next difference as -8:** $$43 - 8 = 35$$ No option matches 35. 20. **Try next difference as -6:** $$43 - 6 = 37$$ Option (b) 37 matches. 21. **Conclusion:** - For first sequence, option (a) 279 fits best. - For second sequence, option (b) 37 fits best. **Final answers:** - First sequence missing term: 279 - Second sequence missing term: 37