Question

The fifth term of an arithmetic progression is -7, and the difference is -3. Calculate the first term and the

Sum of the first 12 terms.

Answer 1

Answer: a₁=5, S₁₂=-138.

Explanation:

The fifth term of an arithmetic progression a₅=-7.

The difference d=-3.

Calculate: a) the first term a₁; b) sum of the first 12 terms S₁₂.

a)

`\boxed {a_n=a_1+(n-1)*d}`

a₅=a₁+(5-1)*(-3)

a₁+4*(-3)=-7

a₁-12=-7

a₁=5.

b)

`\displaystyle\\\boxed {S_n=(2a_1+(n-1)*d)/(2)*n }`

`\displaystyle\\S_(12)=(2 *5+(12-1)*(-3))/(2)*12\\\\ S_(12)=(10+11*(-3))/(2)*12\\\\ S_(12)=(10-33)/(2)*12\\\\ S_(12)=(-23*12)/(2) \\\\S_(12)=-23*6\\\\S_(12)=-138.`