Question

if the 10th term of an ap is 52 and 17th term is 20 more than the 13 term find the AP
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Answer 1

$T_{17} - T_{13} = 20 \\ \\ = (17 - 13)d = 20 \\ \\ = 4d = 20 \\ \\ d = \frac{20}{4} = 5 \\ \\ \\ T_{10} - T_1 = (10 - 1)d \\ \\ = 52 - T_1 = 9 \times 5 \\ \\ = 52 - T_1 = 45 \\ \\ T_1 = 52 - 45 = 7 \\ \\ \\ T_2 = 7 + 5 = 12 \\ \\ T_3 = 12 + 5 = 17 \\ \\ \\ \therefore 7,\ 12,\ 17,......\ is\ the\ AP.$

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