Find the 20 term of the AP whose 3 term is 7 and the 7 term exceed thr

1.	Find the 20 term of the AP whose 3 term is 7 and the 7 term exceed three times the 3term by 2.
Answer» Answer: The 20th TERM of the AP is 75. Step-by-step explanation: The nth term of an AP is: $T_{n}=a+(n-1)d$ It is provided that: $T_{3}=7\\T_{7}=3T_{3}+2$ Substitute the value of T₃ in T₇ and SOLVE as follows: $T_{7}=3T_{3}+2\\a+(7-1)d=3(a+(3-1)d)+2\\a+6d=3a+6d+2\\a=3a+2\\-2a=2\\a=-1$ Compute the value of d as follows: $T_{3}=7\\a+(3-1)d=7\\-1+2d=7\\2d=8\\d=4$ Compute the 20th term as follows: $T_{20}=-1+(20-1)\times4=-1+76=75$ Thus, the 20th term of the AP is 75.