The common difference of an arithmetic sequence is the differwnce between two consecutive terms in a sequence. An arithmetic sequenceis a given of numbers formed by addition or subtraction of a common difference to previous terms.
Now, we get the common difference its d = 3, Then lets find the 45th term of arithmetic sequence of 4, 7, 10, 13, 16 using the formula of Arithmetic Sequence or the General Term given by :
Answers & Comments
Answer:
d=a2-a1
d=7-4
d=3
Step-by-step explanation:
CHECK:
a1+common difference(3)
4+3=7
[tex]\mathbb{SOLUTION:}[/tex]
The common difference of an arithmetic sequence is the differwnce between two consecutive terms in a sequence. An arithmetic sequence is a given of numbers formed by addition or subtraction of a common difference to previous terms.
[tex]\begin{aligned} & \bold{The \: common \: difference \: between \: each \: term:} \\ & \quad \quad \quad \boxed{\begin{array}{l} \rm{a_{2} - a_{1} \implies 7 - 4 = 3} \\ \rm{a_{3} - a_{2} \implies 10 - 7 = 3} \\ \rm{a_{4} - a_{3} \implies 13 - 10 = 3} \\ \rm{a_{5} - a_{4} \implies 16 - 3 = 3} \end{array}}\end{aligned}[/tex]
Now, we get the common difference its d = 3, Then lets find the 45th term of arithmetic sequence of 4, 7, 10, 13, 16 using the formula of Arithmetic Sequence or the General Term given by :
[tex]\begin{aligned} & \bold{Formula:} \\ & \quad \boxed{\begin{array}{l} \rm{A_{n} = a_{1} + (n - 1)d} \end{array}}\end{aligned}[/tex]
[tex]\begin{gathered}{\begin{array}{l} \quad \rm A_{45} = 4 + (45 - 1)3 \\ \\ \quad \rm A_{45} = 4 + (44)3 \\ \\ \quad \rm A_{45} = 4 + 132 \\ \\ \quad \rm A_{45} = \boxed{\green {136}} \end{array}}\end{gathered}[/tex]
Hence, the common difference is d = 3 and the 45th term are 136.