Question

if 7 times of 7 term of AP is equal to 11 times the 11th term then its 18term will be will be

Answer 1

Hey friend,

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Let the first term be a and common difference be d.

T₇ = a + (7-1)d

= a + 6d

7 * T₇ = 7*(a+6d)

= 7a + 42d ------------------------(i)

T₁₁ = a + (11-1)d

= a + 10d

11 * T₁₁ = 11*(a +10d)

= 11a + 110d ------------------------(ii)

(i) = (ii)

7a + 42d = 11a + 110d

4a = 68d

a = 17d

T₁₈ = a + (18-1)d

= a + 17d

= 17d + 17d {a = 17d}

= 34d

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Hope this helped you !!