Question

Question 5 Write the first five terms of the sequences whose nth term is an = (-1)^(n-1) 5^(n+1)

Class X1 - Maths -Sequences and Series Page 180

Answer 1

$a_n=(-1)^{(n-1)}.5^{(n+1)}\\\\\\1st-term(a_1)=(-1)^{(1-1)}.5^{(1+1)}\\a_1=(-1)^0.5^2\\a_n=1.25\\a_n=25\\\\2nd-term(a_2)=(-1)^{(2-1)}.5^{(2+1)}\\a_2=(-1)^1.5^3\\a_2=-125\\\\3rd-term(a_3)=(-1)^{(3-1)}.5^{(3+1)}\\a_3=(-1)^2.5^4\\a_3=1.625\\a_3=625\\\\4th-term(a_4)=(-1)^{(4-1)}.5^{(4+1)}\\a_4=(-1)^3.5^5\\a_4=-1.3125\\a_4=-3125\\\\5th-term(a_5)=(-1)^{(5-1)}.5^{(5+1)}\\a_5=(-1)^4.5^6\\a_5=1.15625\\a_5=15625$