An arithmetic sequence has terms a3 = 11.7 and a8 = −14.6. What is the first term?

Expert Solution

Consider an arithmetic sequence with a3 = 11.7 and a8 = -14.6.

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

Substitute n = 3 and a3 = 11.7 in formula (1) an = a1 + (n – 1)d and simplify,

a3 = a1 + (3 – 1)d

11.7 = a1 + 2d ...... (2)

Substitute n = 8 and a8 = -14.6 in formula (1) an = a1 + (n – 1)d and simplify,

a8 = a1 + (8 – 1)d

-14.6 = a1 + 7d ...... (3)

Subtract equation (2) from equation (3)

-14.6 = a1 + 7d

11.7 = a1 + 2d

-26.3 = 5d

Division by 5 gives,

d = -26.3/5

= -5.26

Substitute d = -5.26 in equation (2) 11.7 = a1 + 2d and solve,

11.7 = a1 + 2 × (-5.26)

11.7 = a1 – 10.52

a1 = 11.7 + 10.52

= 22.22

Therefore, first term of given sequence is a1 = 22.22.

Junaid answered 1 year ago

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