Question

In an AP the ratio of 7th term to the 10th term is -1 and 16th term is -15 what is the third term

Answer 1

Step-by-step explanation:

Find the value of m so that the quadratic equation px^2 + (p – 1) x +(p – 1) = 0 has equal roots.

Answer 2

Answer: 11

Step-by-step explanation:

Formula for nth term of an AP: Tn = a+(n-1)d

{a: first term; n: position of term; d: common difference}

From second information (T16 = —15):

a+15d = —15

Hence, a = —15(d+1) → Equation (1)

From first information (T7/T10 = —1):

(a+6d)/(a+9d) = —1

a+6d = -a-9d

2a = -15d → Equation (2) and substituted by (1):

Therefore, 2(-15d-15) = -15d

-30d-30 = -15d

-15d = 30

d = —2

Thus, a = —15(—2)—15 = 15

Finally, calculate T3:

T3 = a+2d = 15+2(—2) = 11

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