the difference between the 12th and 7th term of an AP is 10. find common difference.
Answers
EXPLANATION.
Difference between the 12th and 7th term of an ap = 10.
As we know that,
General term of an ap.
⇒ Tₙ = a + (n - 1)d.
Using this formula in the equation, we get.
⇒ T₁₂ = a + (12 - 1)d.
⇒ T₁₂ = a + 11d.
⇒ T₇ = a + (7 - 1)d.
⇒ T₇ = a + 6d.
⇒ T₁₂ - T₇ = 10.
⇒ (a + 11d) - (a + 6d) = 10.
⇒ a + 11d - a - 6d = 10.
⇒ 11d - 6d = 10.
⇒ 5d = 10.
⇒ d = 2.
Common difference of an ap = d = 2.
MORE INFORMATION.
Supposition of terms in an ap.
(1) Three terms as : a - d, a, a + d.
(2) Four terms as : a - 3d, a - d, a + d, a + 3d.
(3) Five terms as : a - 2d, a - d, a, a + d, a + 2d.
Answer:
EXPLANATION.
Difference between the 12th and 7th term of an ap = 10.
As we know that,
General term of an ap.
Tn = a + (n - 1)d.
Using this formula in the equation, we
get.
→ T₁2 = a +(12-1)d.
⇒ T₁2 = a + 11d.
T, = a + (7-1)d. T₂ = a + (7 - 1)d.
⇒ T₁ = a + 6d.
T12 - T7 = 10.
(a + 11d) - (a + 6d) = 10.
→a +11d - a - 6d = 10.
→ 11d 6d = 10.
→ 5d = 10.
=> d = 2.
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Common difference of an ap = d = 2.
MORE INFORMATION.
Supposition of terms in an ap.
(1) Three terms as : a - d, a, a + d.
(2) Four terms as : a - 3d, a - d, a +d, a +
3d.
(3) Five terms as : a - 2d, a - d, a, a + d, a + 2d.