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In an A.P., the first term is a and the common difference is d. Express a in terms of d given that A14 = 5A2.

Mathematics

ScanSolve AI Answer

a) Find a simplified equation of aa in terms of dd.

Step 1: Express the terms of the A.P.
Let the first term of the A.P. be A1=aA_1 = a and the common difference be dd.
The nn-th term of an A.P. is given by An=A1+(n−1)dA_n = A_1 + (n-1)d.
The 2nd term of the A.P. is A2=a+(2−1)d=a+dA_2 = a + (2-1)d = a+d.
The 14th term of the A.P. is A14=a+(14−1)d=a+13dA_{14} = a + (14-1)d = a+13d.
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